Preheat oven to 400 degrees F. In a large pot of boiling water, cook gnocchi according to package directions; drain and set aside.
Season chicken with salt and pepper. Melt 2 Tablespoons butter in a large, oven-safe skillet over medium-high heat. Add chicken to the skillet and cook until golden brown, about 4-5 minutes, on each side and cooked through. Remove cooked chicken from the skillet and set aside.
In the same skillet, add remaining 2 Tablespoons butter. Add onion and cook for 3-5 minutes, or until tender. Add garlic and thyme and cook for an additional minute. Whisk in flour and cook for 2 minutes, or until golden brown.
Gradually whisk in chicken broth and cook for 3-5 minutes, or until thickened. Whisk in milk and season with salt and pepper to taste.
Add cooked gnocchi and spinach to the skillet and stir until spinach has wilted. Add chicken back to the skillet and top with Parmesan cheese. Place skillet in the oven and bake for 10 minutes.