Preheat oven to 425 degrees.
Cut spaghetti squash in half and scoop out the seeds. Place on a baking sheet face up. Drizzle with olive oil, salt, pepper, and place one garlic clove inside each half. Turn over on baking sheet so that the squash is cut side down. Bake for 45 minutes.
While squash is baking, cut chicken breasts into cubes. Season with salt, pepper, onion powder, and a pinch of red pepper.
Heat a large skillet with butter and a drizzle of olive oil. Add chicken cubes and mushrooms to the skillet. Cook until chicken has browned on both sides. Remove chicken and mushrooms from skillet and set aside.
Add chopped garlic and thyme to the skillet and cook over medium-low heat until fragrant, about 3 minutes. (If pan needs more oil, add additional butter and olive oil) Add flour and mix together until a loose paste forms, about 2-3 minutes. Then add heavy cream and parmesan. Whisk together constantly.
Once sauce thickens, slowly add chicken broth, whisking constantly. (If sauce breaks apart for a few seconds, keep whisking, it will come back together.)
Remove spaghetti squash from the oven and use a fork to flake up the spaghetti squash strands. Mash the roasted garlic into the squash.
Pour Alfredo sauce into each half of the spaghetti squash. Place chicken and mushrooms on top of sauce as well as additional fresh thyme
Sprinkle with mozzarella cheese and place in the oven for 10 minutes. Then broil on the top rack of the oven for about 2-3 minutes (watch closely so as not to burn).