Slice each chicken breast horizontally to create four thin cutlets.
In a shallow bowl, combine the flour, salt, garlic powder, and black pepper.
Coat each chicken cutlet evenly in the seasoned flour and shake off the excess.
Heat the olive oil and butter in a large skillet over medium-high heat.
Cook the chicken for 3–4 minutes per side until golden and nearly cooked through. Remove and set aside.
Reduce the heat to medium and sauté the diced shallots until soft and fragrant.
Stir in the chicken stock, heavy cream, and Parmesan cheese. Simmer for 2–3 minutes until slightly thickened.
Add the cherry tomatoes and cook until they begin to soften.
Lower the heat and stir in the pesto until smooth and creamy.
Return the chicken and any juices to the skillet, coating each piece in the Creamy Pesto Chicken sauce.
Simmer for another 2–3 minutes until the chicken is fully cooked.
Serve immediately with your favorite side dishes.