Pat chicken cutlets dry with paper towels. Season both sides with salt and pepper.

Set up 3 shallow bowls: flour in the first, beaten eggs in the second, and breadcrumb-Parmesan mixture in the third. Dredge each cutlet in flour, dip in egg, then press firmly into the breadcrumb mixture on both sides.

Heat olive oil in a large skillet over medium heat. Add chicken in a single layer and cook for 3 to 4 minutes per side until golden brown and cooked through to 165 degrees F. Cook in batches if needed. Transfer to a plate.

In the same skillet, reduce heat to medium-low. Melt butter, add garlic, and cook for about 1 minute until fragrant but not browned.

Add chicken broth and stir to deglaze the pan. Pour in heavy cream and Parmesan. Simmer for 3 to 5 minutes, stirring often, until sauce thickens. Taste before seasoning with salt and pepper.

Return chicken to the skillet and spoon sauce over each piece. Garnish with fresh parsley or thyme. Serve immediately.