One-Pan Creamy Chicken & Gnocchi

Season chicken on both sides with salt and pepper. In a large skillet over medium-high heat, heat 1 tablespoon oil. Add chicken and cook until golden, 4 minutes per side. Remove from skillet.  Reduce heat to medium and add remaining 1 tablespoon oil. Add shallot and mushrooms and cook until golden, 5 minutes. Add garlic, thyme, and oregano and cook until fragrant, 1 minute more. Add broth and scrape up any brown bits on bottom of pan, then slowly add in half and half. Bring to a simmer and season with salt, pepper, and a pinch of red pepper flakes. Stir in gnocchi and return chicken to pan. Let simmer until chicken is cooked through and internal temperature reaches 165°, 8 to 10 minutes, stirring occasionally. Remove chicken from skillet.  Add cheeses and stir until melted, then add spinach and stir until wilted.  Slice chicken and return to skillet. Season with more salt and pepper to taste.