Prepare the chicken by rinsing, drying, and slicing pockets into each chicken breast. Season with salt, pepper, and garlic powder.
Wrap the chicken in prosciutto, securing with toothpicks if necessary.
Make the pesto cream sauce by heating heavy cream and adding basil pesto. Simmer for 5 minutes.
Sear the prosciutto-wrapped chicken in olive oil for 3-4 minutes on each side until golden brown.
Transfer the skillet to the oven and bake for 20-25 minutes until the internal temperature reaches 165°F.
Let the chicken rest for 5 minutes before slicing and serving with the pesto cream sauce.