Pat chicken pieces dry and season with salt and pepper. Heat 1 tablespoon olive oil in a large deep skillet over medium-high heat. Add chicken in a single layer and cook undisturbed for 4 minutes until golden brown. Flip and cook 3 minutes more until cooked through. Transfer to a plate and set aside.

Bring a large pot of salted water to a boil. Cook penne according to package directions until al dente, usually 10-11 minutes. Reserve 1 cup pasta water, then drain and set aside.

In the same skillet used for chicken, reduce heat to medium and add butter and remaining 1 tablespoon olive oil. Add garlic and red pepper flakes if using; cook 30 seconds until fragrant but not browned. Pour in heavy cream and simmer for 3-4 minutes, stirring occasionally, until slightly thickened.

Stir in Parmesan until melted and smooth, about 1 minute. Add spinach by handfuls, stirring until wilted, 2-3 minutes total. The sauce will look thick; this is normal.

Add cooked pasta and chicken to the skillet, tossing to coat. Add reserved pasta water a splash at a time until the sauce clings to the pasta, about 1/4 to 1/2 cup total. Cook 1-2 minutes more until everything is heated through and glossy. Taste and adjust salt as needed.

Divide among bowls and top with extra Parmesan. Serve hot.