Place a chicken breast half, boned side up, between 2 pieces of plastic wrap. Working from the center to the edges, pound lightly with the flat side of a meat mallet to 1/8-inch thickness. Remove plastic wrap. Sprinkle chicken lightly with black pepper. Repeat with remaining chicken.
Firmly squeeze spinach until well drained and practically dry. (I wrap in clean kitchen towel and wring moisture out.) In a small bowl, combine 1/2 of the spinach and egg. (Save remaining chopped spinach for Sautéed Spinach Cream Sauce.)
For each roll, spoon about 2 tablespoons of the spinach mixture onto each chicken piece, spreading evenly over chicken. Top with a slice of prosciutto or . Place a stick of cheese near an edge. Fold in sides; roll up, starting from edge with cheese, into a spiral, pressing the edges to seal. Secure with wooden picks. Place rolls, seam side down, in a 13x9x2-inch (3-quart) baking dish. Drizzle with butter.
Bake, uncovered, in a preheated oven for 35 to 40 minutes or until chicken is no longer pink (170 degrees). Remove toothpicks. Meanwhile, prepare Spinach Cream Sauce.
To serve, slice each chicken roll. Transfer chicken to a dinner plate. Top with cream sauce.
Sautéed Spinach Cream Sauce: In a medium saucepan, melt butter over medium heat. Add garlic and cook 1 minute; add the remaining chopped spinach. Cook and stir for 5 minutes. Add whipping cream, kosher salt and freshly ground black pepper. Cook and stir for 30 seconds or until heated through. Serve over chicken.