Green Bean and Potato Pie

We understand that green beans vastly prefer being called haricots verts, and while we don't blame them, we're going to stick with what we know. There is a classic Genovese recipe that involves mashing them with potatoes, adding some eggs and cheese, and baking them off. It's good, but we wanted to enhance it to make a good vegetarian main dish. The results, this pie, were delicious. And yes, if you want to serve it to foodie friends, it's ok to call this a "tarte de pommes de terre et haricots verts."

Green Bean and Potato Pie

½ lb green beans, preferably a thin varietal
5-6 medium red potatoes, quartered
1 medium red onion, sliced thin
1 carrot, cut into tiny cubes
1 ½ cups milk
1 cup grated Swiss cheese
Brie cheese (3 oz or so, optional))
1 tbsp butter
2 tsp flour
2 eggs
Breadcrumbs or crumbled Ritz crackers
Salted creole seasoning (Tony Chachere's)

1. Bring a stockpot full of salted water to boil. Add the green beans and cook until tender. Remove with a slotted spoon and drain.
2. Preheat your oven to 350.
3. Quarter the potatoes and add them to the stock pot. Cook until tender.
4. Put the green beans through a food mill. If some doesn't go through, don't worry, you just want them nice and mashed.
5. Put the potatoes through the food mill and toss with green beans.
6. Add the carrots to the bowl and toss.
7. Add creole seasoning to taste.
8. In a frying pan, melt the butter, add the flour, then add the milk while whisking to create a loose béchamel sauce.
9. Add the shredded cheese slowly and stir to melt. (French cooks would refer to this a sauce Mornay.)
10. Add the onions and allow them to infuse the sauce-it should be loose , but not watery. (French cooks would not refer to this as a sauce Mornay.)
11. Beat the eggs together in a bowl with a little water. Add a tablespoon of the hot sauce, and mix to combine. Repeat this step until the eggs are warm and well incorporated with cheese sauce. Then add the egg mixture to the rest of the hot sauce and stir to incorporate. This process is known as tempering, and it keeps you from scrambling the eggs.
12. Add creole seasoning to taste.
13. Pour one third of the sauce in with the potatoes and green beans and mix.
14. Grease a casserole dish. Add one half of the potato mixture and spread into an even layer.
15. Place slices of brie over the layer to cover.
16. Pour over one half of the remaining sauce.
17. Add the rest of the potatoes and smooth over to cover.
18. Add the remainder of the cheese sauce. Top with bread crumbs.
19. Bake for 20 minutes in the oven. If the top starts to brown, cover with aluminum foil.
20. Remove and allow to rest five minutes before serving.