Preheat oven to 400F. Bring a large pot of salted water to a boil; boil pasta to al dente according to package directions, draining and setting aside.
In a large saucepan, melt butter over high heat. Add mushrooms, and season with salt and pepper. Cook, stirring frequently, for 4 minutes, then add onion and garlic. Continue cooking for 4-5 minutes, until tender and browned.
Reduce heat to medium and sprinkle the flour over the vegetables. Stir for 30 seconds, then add the milk. Stirring constantly, add the sour cream, broth, and wine. Bring the mixture to a boil, then reduce to a simmer until it begins to thicken. Remove from heat.
Stir in 1 ¼ cups colby jack and thyme, then season with salt and pepper to taste.
Add chicken and pasta to the sauce, tossing to combine.
Transfer to a 9x13 baking dish. Sprinkle with remaining cheese. Bake for 25-30 minutes, or until browned. Let stand 10 minutes before serving.