Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs, then drain.
Reserve a cup of boiled pasta water. Toss spaghetti in a tablespoon of olive oil and set aside.
Melt 2 tablespoons of butter in a large skillet over medium-high heat.
Add the garlic, onion and cook until slightly soft, about 2 minutes.
Add the mushrooms and cook, stirring, until they begin to brown, about 2 minutes.
Add the remaining 1 tablespoon butter, flour and chili flakes. Cook, stirring for a minute.
Now add the chicken, salt and pepper. Cook, stirring, until the chicken browns, about 3 - 5 minutes.
Add the reserved pasta water, thyme and bring to a gentle simmer.
Stir in the cream. Continue simmering gently until the chicken is cooked through.
To serve, divide the spaghetti among plates. Top with the chicken stroganoff and white sauce.
Serve Chicken Stroganoff with Spaghetti warm garnished with grated cheese.