Challenge for you all: items in my fridge I need to use up!

http://allrecipes.com/recipe/8547/chicken-in-basil-cream/, with bell peppers added to it.

For cabbage, I'll roast the cabbage and serve it as a side. CI's recipe is really good and simple http://community.cookinglight.com/archive/index.php/t-130962.html

Add vinegar or lemon juice to your heavy cream for a diy buttermilk. Marinate the chicken breasts in it (maybe with some lemon pepper) reserving just a bit of the 'buttermilk'. Use the basil, bell peppers, cabbage for a simple slaw (dressed with reserved buttermilk). Bread (or not) the chicken and fry/bake.

For me it would depend on the amount of cream, I don't usually buy cream in amounts larger than a pint so my two suggestions are for less than 1/2 cup and more than 1/2 cup.

Less than 1/2 cup: Stuff the peppers! I like to make "quiche peppers" where the pepper is the crust but even if you don't have any eggs a stuffed pepper is great. Poach and then shred the chicken if it's got bones and skin or cut into little bites and brown them if it is boneless. Stir together with the basil (torn or julienned) cream and any cheese, eggs, and aromatics you have on hand. Cooked grains or rice are also good. For more texture top with cheese/breadcrumbs. Bake in 375 oven for 35minutes or until very fragrant and bubbly

More than 1/2 cup: A very decadent chicken alfredo! Smash some garlic and then gently heat the cream until steaming cover and let steep for 20-30 min while you cook the chicken. Roast it if there's skin, poach or braise if not. Strain the garlic from the cream and turn into a bechamel, thin with water, milk, stock or white wine if there are more eaters than yourself. Pour the sauce over noodles or grains top with the chicken, sliced, and garnish with the basil. If you have more basil than just for a garnish, make a salad with the cabbage and pepper.

Have a safe trip!
http://www.myfriendmaillard.com/

Not sure if your chicken in bone-in or not, or if the bell peppers are red or green (in my imagination they're red, so I'll go with that). I could see charring the peppers either over a gas burner or under the broiler, then letting them steam a bit in a ziploc bag and, once they're cool enough to handle, peeling off the charred skin, cutting then open to remove the seeds and pith, and then pureeing in a blender, maybe with some charred or caramelized onion and a little roasted garlic. You could then reduce the red pepper sauce a bit in a skillet, add the chicken (if it's skin on it would be a good idea to sear the chicken first), then cover and braise until the chicken is cooked. Once cooked, remove the chicken, adjust sauce for seasoning and finish with a little of the cream and the basil. Serve over rice or pasta. Cabbage will keep forever so I wouldn't worry as much about leaving it in the fridge, OR (just had an idea!) you could add a little chili powder to the pepper sauce and shred the chicken to use in a taco, and make a little Mexican-style slaw out of the cabbage. The basil might be weird in that case, though...

As a card-carrying member of the Keep It Simple Party, I'd personally saute the bell peppers and cabbage, add the basil at the end. If you want, you could add some spiciness/exoticity (sriracha, lemon juice, hot sauce, garlic, ginger, soy, whatever).

As for the other ingredients, I'd brown & braise the chicken breasts (maybe toss in some onion), add the cream at the end for a richer sauce.

I typically don't use recipes, however I know what my taste buds like. It's really a personal decision for these sort of situations. There are a bazillion ways to handle these ingredients.

Anyhow, good luck.

Try this recipe: http://www.epicurious.com/recipes/food/views/mustard-cream-sauce-5427 I have made it many times (though not in a few years). It is a great sauce for a pounded, sauteed chicken breast or a piece of fish. If the bell peppers are red, try roasting them over an open gas flame or under the broiler, then put them in a bowl, tightly covered with plastic for 10-15 min. Let them steam to loosen the charred skins. Then remove the skins and seeds/membranes (but don't rinse or you will lose all the great roasted pepper flavor). Chop roughly and add to the sauce just before you put the sauteed chicken in. If the peppers are green, make a cabbage salad with chopped cabbage and peppers and poppyseed dressing.