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Preheat oven to 350 degrees.
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Bring a large pot of water to boil and cook tortellini according to directions. Drain.
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Pour the tortellini into the bottom of a 2 quart casserole dish. Sprinkle half of the grated cheese over the tortellini.
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In a large frying pan, melt 2 Tablespoons of the butter over medium heat. Toss the chicken chunks with the flour to coat them (save the flour), then cook them in the butter until the outsides are nicely browned. Layer the chicken chunks on top of the tortellini and cheese.
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In the frying pan, melt the remaining 2 Tablespoons of butter and stir in the diced onion (and mushrooms, if you're using them), cooking for about 3 minutes. Sprinkle the flour leftover from the chicken on top and stir to combine. Let cook for about 2 more minutes, then add the chicken broth. Bring to a low boil so that it thickens.
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Stir in the sour cream and remaining grated cheese. Stir until smooth, then pour over the top of the casserole.
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Bake for 25-30 minutes.