In a shallow bowl, combine the flour, garlic powder, 1/2 teaspoon salt, and 1/2 teaspoon pepper.
Lightly coat both sides of each chicken cutlet with the seasoned flour mixture and shake off excess.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat until hot.
Add the chicken to the skillet in a single layer and cook 3–4 minutes per side until golden and cooked through; remove chicken and set aside.
Reduce heat to medium, add the pressed garlic to the skillet, and cook about 30 seconds until fragrant.
Pour in the heavy cream and add the grated Parmesan; bring to a gentle boil, stirring frequently for about 2 minutes.
Lower the heat and stir in the prepared pesto until the sauce is smooth and combined.
Return the chicken to the skillet, nestling pieces into the sauce, and simmer 3–5 minutes until the sauce thickens and chicken is heated through.
Stir in the quartered grape tomatoes, sprinkle with chopped fresh basil, and serve immediately.