Pat the chicken dry with a paper towel. Season with salt and pepper.
Heat a large frying pan over medium-high heat. Add the olive oil. When hot add the chicken to the pan and cook for 3-4 minutes per side. Transfer the chicken to a plate.
Melt butter in the pan. Add onion and cherry tomatoes and cook until softened, about 5 minutes. Add garlic and cook until fragrant, about 1 minute.
Pour in chicken broth and cream. Whisk any browned bits from the bottom of the pan. Add the spinach. Cook for 10-15 minutes, until bubbly and slightly thickened. Add the Parmesan cheese and whisk again to combine.
Return chicken to the pan. Spoon sauce over the chicken to coat. Cook 1-2 minutes, until chicken is warmed. Serve with fresh parsley and red pepper flakes as garnish.
Serve alongside cauliflower rice or steamed broccoli, or with low-carb noodles.