Place one butterflied chicken breast on top of plastic wrap with cut-side of chicken facing up.
Place 2 slices of prosciutto on top of butterflied chicken breast, overlapping prosciutto slices as needed to fit within edges of chicken breast.
Cover prosciutto evenly with 3 ounces goat cheese. Overlap goat cheese slices as needed to fit within edges of chicken breast.
Sprinkle ¼ tablespoon Italian seasoning evenly across top of goat cheese, then cover goat cheese evenly with ¼ cup baby spinach leaves.
Rotate plastic wrap so that short side of chicken breast faces toward you. Starting from closest edge of chicken breast and working slowly, roll chicken breast away from you without picking up plastic wrap. Roll chicken tightly, creating spiral.
Once chicken breast is rolled, place chicken seam-side down. Carefully slide 2 to 4 pieces of twine under chicken roll, being careful not to unroll chicken. Wrap each piece of twine around chicken and tie twine tightly to hold roll closed.
Set rolled chicken breast aside and repeat process with remaining 3 chicken breasts.
Once all chicken breasts have been rolled and tied, liberally season each chicken roll on all sides with salt and pepper.