Preheat oven to 425°F.
Lay chicken breasts flat and place 1 to 2 pieces of prosciutto on top. Top with 1/4 cup shredded cheese to each breast and a sprinkle of basil, some salt and pepper.
Roll each breast lengthwise and secure with toothpicks or three to four pieces of kitchen twine: Tie one on each end to close and one or two in the middle.
Heat a frying pan with olive oil over high heat and sear the chicken rolls on all sides, about 1-2 minutes on each side or until medium brown and lightly crispy.
Place chicken on a baking sheet and transfer to oven to cook through, about 15 minutes
Allow the chicken rolls to rest a few minutes before removing the twine. To serve, cut each breast at a sharp angle, yielding 6 to 8 roulades.