Hardlikearmour's carnitas are a good bet, but coincidentally, I just made pork jambalaya tonight, in MY LeCruset, and it was awesome.

1 T veg oil
1-ish pounds boneless pork country ribs (sub pork shoulder), cut into 2" pieces, heavy fat trimmed
Salt, pepper, Tabasco
3/4C chopped yellow onion
1/4C-ish chopped celery
3 cloves garlic, peeled & minced
1/2C-ish chopped green bell pepper
1/2C-ish canned, diced tomatoes
2C chicken broth
1/4C thinly sliced green onions (white & green parts)
3T-ish chopped fresh parsley
3/4C rice

Heat oil in Dutch oven. Season pork cubes with about 1/2T salt, 1/2 tsp. pepper and 1/2 tsp. Tabasco. When oil is hot, add meat, cook, covered, over medium heat until pork is well browned all over, about 45 minutes, stirring and flipping meat as needed. Be careful, it will be hot, and it will sputter.

Remove pork from pan, reserve in bowl or on plate. Either reserve about 1&1/2T fat, or add enough additional oil to that point. Add onion, and sautee over med heat until translucent, about 5 min., scraping up browned goodness from bottom. Add celery and garlic, and sautee another 3 minutes, stirring and scraping up brown goodies occassionally. Add green pepper and sautee another 2 or 3 minutes, scraping pan occassionally.

Add tomatoes and return pork to pan. Stir well, bring to simmer, cover and cook over low heat (low simmer) for 30 minutes. Add broth, bring to a boil and simmer (low simmer) over low heat another 30 minutes. Add green onions, parsley, 1/4 tsp. pepper, 1/2 tsp salt, 1 tsp. Tabasco and rice. Stir wel, bring to boil, and reduce heat to very low. Simmer, covered, 25-30 minutes, or until rice is cooked. Remove from heat, let sit 5 minutes covered, and serve with additional green onions, parsley and Tabasco as garnish/to taste. Yummy ! :-)

Thanks everyone for your excellent ideas!!! I found my new little dutch oven for $30 dollars! Crazy price, I know! : )

You can hardly go wrong with a pork shoulder and a Le Creuset! This recipe is amazing and plays to Le Creuset's strengths--long slow cooking in two phases, one in the oven, the second on the stovetop. It is a very simple preparation over two days. Rancho Gordo has wonderful dried posole, which is what I use in the recipe. And of course, it's a perfect meal for this time of year.
http://www.epicurious.com/recipes/food/views/Holiday-Pork-Posole-350820

I'm a huge fan of pulled pork:

Mexican Pulled Pork (Carnitas)

Serves 6. Published May 1, 2008. From Cook's Illustrated.

We like serving carnitas spooned into tacos, but you can also use it as a filling for tamales, enchiladas, and burritos.

Pork
1 (3 1/2-to 4-pound) boneless pork butt , fat cap trimmed to 1/8 inch thick, cut into 2-inch chunks
1 teaspoon ground cumin
1 small onion , peeled and halved
2 bay leaves
1 teaspoon dried oregano
2 tablespoons juice from 1 lime
2 cups water
1 medium orange , halved
Tortillas and Garnishes
18 (6-inch) corn tortillas , warmed
Lime wedges
Minced white or red onion
Fresh cilantro leaves
Thinly sliced radishes
Sour cream
Instructions

1. Adjust oven rack to lower-middle position and heat oven to 300 degrees. Combine pork, 1 teaspoon salt, 1/2 teaspoon pepper, cumin, onion, bay leaves, oregano, lime juice, and water in large Dutch oven (liquid should just barely cover meat). Juice orange into medium bowl and remove any seeds (you should have about 1/3 cup juice). Add juice and spent orange halves to pot. Bring mixture to simmer over medium-high heat, stirring occasionally. Cover pot and transfer to oven; cook until meat is soft and falls apart when prodded with fork, about 2 hours, flipping pieces of meat once during cooking.

2. Remove pot from oven and turn oven to broil. Using slotted spoon, transfer pork to bowl; remove orange halves, onion, and bay leaves from cooking liquid and discard (do not skim fat from liquid). Place pot over high heat (use caution, as handles will be very hot) and simmer liquid, stirring frequently, until thick and syrupy (heatsafe spatula should leave wide trail when dragged through glaze), 8 to 12 minutes. You should have about 1 cup reduced liquid.

3. Using 2 forks, pull each piece of pork in half. Fold in reduced liquid; season with salt and pepper to taste. Spread pork in even layer on wire rack set inside rimmed baking sheet or on broiler pan (meat should cover almost entire surface of rack or broiler pan). Place baking sheet on lower-middle rack and broil until top of meat is well browned (but not charred) and edges are slightly crisp, 5 to 8 minutes. Using wide metal spatula, flip pieces of meat and continue to broil until top is well browned and edges are slightly crisp, 5 to 8 minutes longer. Serve immediately with warm tortillas and garnishes.

This is INCREDIBLE - http://www.food52.com/recipes/3909_matilda_maple_garlic_pork_shoulder_with_crispy_skin

I would cut the recipe in half or thirds to accommodate the smaller size.

I rather like this done with pork instead of beef. Easy, but exactly the kind of thing your new Creuset was made for!

http://www.nytimes.com/2010/12/05/magazine/05food-t-001.html?ref=magazine