Butter a 10-inch casserole dish using about 1 teaspoon cultured unsalted butter. Move the oven rack to the middle position and preheat the oven to 500 degrees F (260 C).
1 teaspoon cultured unsalted butter
Bring a large pot of salted water to a rolling boil and add the 180 grams green beans.
180 grams green beans
Blanch the beans by bringing the water back up to a full. Drain the beans and rinse them under cold water to chill them enough to handle.
Trim the stem ends off of the beans and chop them up into 1.5-inch lengths.
Melt 1 tablespoon cultured unsalted butter in a frying pan over medium heat and sauté the 100 grams onions, 120 grams button mushrooms, 100 grams shimeji mushrooms, and 1 teaspoon salt until the mushrooms are starting to caramelize (about 6-7 minutes).
1 tablespoon cultured unsalted butter, 100 grams onions, 120 grams button mushrooms, 100 grams shimeji mushrooms, 1 teaspoon salt
Transfer the mushrooms to a bowl and add the remaining 1 tablespoon cultured unsalted butter to the pan along with the 25 grams flour. Cook the roux until there are no lumps of flour, but don't let it brown.
1 tablespoon cultured unsalted butter, 25 grams flour
Turn down the heat and pour the 1 ½ cups milk in at once. Stir the mixture vigorously until there are no lumps of roux remaining.
1 ½ cups milk
Turn up the heat to medium and bring the béchamel to a boil to thicken. Add the sautéed mushrooms as well as the green beans to the pan, and stir to distribute evenly.
To assemble the Doria, spread an even layer of 350 grams cooked rice along the bottom of the buttered casserole dish.
350 grams cooked rice
Top with the mushroom and green bean béchamel.
Cover with an even layer of 100 grams Gruyere and mozzarella cheese.
100 grams Gruyere and mozzarella cheese
Put the Doria in the oven and bake until the sauce is bubbly and the cheese has browned on top, about 15-20 minutes. Top with Fried onions and serve.
Fried onions