Mix the 1/2 tsp garlic powder, 1/2 tsp salt, and 1/2 tsp black pepper in a small bowl, then season both sides of the chicken cutlets evenly.
Heat 1 tbsp olive oil in a large skillet over medium-high heat until shimmering.
Cook the chicken in a single layer, 3–4 minutes per side, until browned and cooked through; work in batches if needed to avoid crowding. Transfer cooked chicken to a plate and set aside.
Reduce heat to medium, add the pressed garlic to the skillet and cook, stirring, for about 30 seconds until fragrant.
Pour in the 28 oz crushed tomatoes and add 1 tbsp dried Italian seasoning and the remaining 1/2 tsp salt; stir and scrape up any browned bits, then simmer for about 5 minutes.
Stir in 1/4 cup Parmesan and 1/2 cup heavy cream until the sauce is smooth, then stir in the chopped fresh basil.
Return the chicken to the skillet, spoon sauce over the pieces, and simmer, uncovered, 3–5 minutes until heated through and flavors meld.
Serve hot, garnished with additional basil or Parmesan if desired.