Season the chicken pieces with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Cook the chicken for 5-7 minutes on each side until golden brown. Remove and set aside.
In the same skillet, add more olive oil if needed. Lower the heat and sauté the garlic for about 1 minute until fragrant. Add cherry tomatoes and cook for another 3-4 minutes until softened.
Pour in the chicken broth and bring to a gentle simmer. Add the heavy cream and dried oregano, stirring well. Let it simmer for about 5 minutes until slightly thickened.
Stir in the baby spinach and let it wilt into the sauce for about 2-3 minutes.
Return the cooked chicken to the skillet, sprinkle Parmesan on top, and mix gently. Warm through for an additional 2-3 minutes. Adjust seasoning if necessary.
Serve with your favorite pasta or crusty bread to soak up the sauce!