Boil the potatoes in salted water for 15 minutes. Drain and set aside.
Peel & chop the onion.
Melt 1 tablespoon of butter and olive oil in a skillet.
Add the onion and sauté until transparent. Remove onion from pan.
Add remaining 2 tablespoons butter to the pan. Whisk in the flour.
Whisk in milk.
Season with salt and pepper to taste.
Bring to a boil, Add thyme.
Turn the heat down to low. Simmer for 10 minutes. Whisk occasionally.
Preheat the oven to 350F. Grease a 9” x 9” casserole dish.
Rinse the beans.
Mix the potatoes, onions, beans, and half of the cheese and transfer to the casserole dish.
Remove thyme from the béchamel sauce.
Pour the béchamel over the top.
Sprinkle with remaining cheese and bake 30 minutes.
Remove from oven and serve.