Fridge Clean Out: Ready, Set, Go!

Roasted veggie poutine!

Great ideas listed above...or you could do carrot fritters, sweet potato fritters, carrot-sweet potato fritters. Never made parsnip fritters before but it seems like it could work (or you could freeze as mentioned above). The eggs would go into the batter, as could the herbs. You COULD make a cheesy dipping sauce from the two cheeses and evaporated milk, although personally that would be a little heavy for me with a fried dish. If you went that way I'd add some mustard to make it a bit more bracing.

That Parmesan won't spoil in two weeks, but I can see where you'd want to use it to embellish whatever you make with the veggies. Actually, the eggs won't spoil in 2 weeks either - refrigerated.

I like the vegetable gratin idea.
If you have some pasta or stale bread, you could make a noodle pudding or bread pudding, using those of the ingredients you like, and hold it together with eggs & evaporated milk.
Also, FYI, you don't have to use it all up. The carrots & parsnips will freeze well (blanched or raw cut), as will the eggs (in ice cube trays or plastic containers, as whole, whites or yoks), and the Parmesan will also freeze.

It's like the Splendid Table (but with realistic ingredients)! Oh, goodie. Make my blackened carrots and sweet potatoes, adding parsnips with the carrots (https://food52.com/recipes/36441-blackened-honey-glazed-sweet-potatoes-and-carrots). And yes, I know I'm tooting my own horn, but it's really good anyway. Then a omelet with the eggs, cheeses and rosemary. Call the evaporated milk a casualty of vacation and recycle the can so you'll feel ok about it. Have a great great vacation - you all have been burning the candle at both ends for some time now it seems like!

Funny, I just made a clean-out my fridge sweet potato and kale gratin last weekend and it hit the spot. I riffed on the Genius potato gratin by par-cooking the potatoes in half and half, sautéed the kale with lots of garlic and shallots, then layered them in my pan. Topped with panko mixed with grated horseradish, lemon zest, and fresh chopped herbs. I ate the leftovers with a fried egg and hot sauce. You could pretty much do the same thing and add the grated cheese to the panko topping. Let us know what you end up doing!

Roasted root veggies with shirred eggs and cheese.

Oven roast veggies with rosemary & salt. Divide the milk between 4 ramekins, nestle in egg in, grate Parmesan on top. Bake eggs. Divide veggies and top with egg, Monterey Jack, and a few grinds of pepper.