Season chicken thighs evenly with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Sear chicken for 5-6 minutes per side until golden brown, then remove and set aside.
In the same skillet, melt butter. Add onions and mushrooms, sautéing for 8 minutes until softened and browned.
Add minced garlic and cook for 1 minute until fragrant.
Sprinkle flour over the vegetables and whisk for 2 minutes to create a light roux.
Slowly whisk in 1.5 cups of chicken broth and the heavy cream, ensuring no lumps remain.
Add dried thyme and return the chicken thighs to the skillet.
Lower heat and simmer for 12-15 minutes until the sauce has thickened and chicken reaches an internal temperature of 165°F.
While chicken simmers, combine rice and the remaining 0.5 cups of chicken broth (plus 1.5 cups water) in a pot; bring to a boil, then cover and simmer for 15 minutes.
Serve the smothered chicken and gravy over the cooked rice, garnished with fresh parsley.