Preheat oven to 400 degrees F.
Lightly coat a 9x13 baking dish with nonstick spray.
Season chicken thighs with salt and pepper, to taste.
Melt 2 tablespoons butter in a large skillet over medium high heat.
Add chicken, skin-side down, and sear both sides until golden brown, about 2-3 minutes per side.
Place chicken, skin-side up, in a single layer into the prepared baking dish. Place into oven and roast until completely cooked through, reaching an internal temperature of 175 degrees F, about 25-30 minutes. Drain excess fat.
Meanwhile, bring a large pot of salted water to a boil, and cook pasta according to package instructions. (If using fresh pasta, wait until after the sauce is finished).
To make the mushroom sauce, melt remaining tablespoon butter in the skillet. Add mushrooms, and cook, stirring occasionally, until tender and browned, about 5-6 minutes.
Stir in the garlic and continue sautéing for about 1 minute.
Whisk in flour until lightly browned, about 1 minute.
Gradually whisk in half and half, and continue whisking until flour is incorporated and sauce comes together, coating the back of a spoon.
Add thyme and crushed red pepper flakes.
Continue cooking, whisking constantly, until slightly thickened, about 3-4 minutes.
Remove from heat and whisk in Brie slices one-at-a-time until incorporated into the sauce, continue adding until all cheese is mixed in. *If sauce becomes too thick, whisk in some of the pasta water a little at a time until the sauce reaches the desired consistency.
Season with salt and pepper, to taste.
If time remains on the chicken, cover and set sauce aside until chicken is done.
Remove chicken from the oven and spoon over 1/3 of the sauce mixture.
The bowtie pasta should be cooked al dente; drain the remaining pasta water off completely.
Add the drained pasta to the remaining sauce in the pan, as well as the fresh parsley and toss lightly to coat all of the pasta.
To serve, portion pasta onto each plate with the finished chicken on top. Serve immediately.