Stack 2 slices ham on work surface; pat dry with paper towel. Spread evenly with 1 1/2 to 2 teaspoons cream cheese. Top with basil leaves to within 1 inch of top edge. Cut pepper into 1-inch strips; cut to fit width of ham. Place pepper strips across bottom edge of ham. Place cheese piece above pepper on basil leaves; trim to fit.
Beginning at bottom, roll up securely. Wrap in plastic wrap. Repeat with remaining ingredients to make 5 rolls. Refrigerate 2 hours.
Unwrap rolls; place seam sides down. Cut each roll into 5 pieces with sharp serrated knife. If desired, pierce each roll with 5 evenly spaced toothpicks before cutting.