Pat the chicken cutlets dry and season both sides with 1/2 teaspoon salt, 1/2 teaspoon garlic powder, and 1/2 teaspoon black pepper.
Heat a large skillet over medium heat and add 1 tablespoon olive oil.
When the skillet is hot, add the chicken in a single layer without crowding and cook 3–4 minutes per side until an instant-read thermometer reads 165°F; work in batches if needed. Remove cooked chicken and set aside.
Reduce heat to low, add 3 tablespoons butter to the skillet and let melt. Stir in 1 tablespoon flour until combined.
Add the pressed garlic and cook 30–60 seconds until fragrant, then slowly whisk in 1/2 cup chicken broth and bring to a gentle simmer to thicken.
Stir in 3/4 cup heavy cream, the remaining 1/2 teaspoon salt, 1/4 cup parmesan, chopped sun-dried tomatoes, and 1/4 cup chopped basil. Simmer until sauce is warmed and slightly thickened.
Return the cooked chicken to the skillet and simmer in the sauce 3–5 minutes to heat through and meld flavors.
Serve immediately, optionally garnished with extra basil or parmesan.