Heat dinner rolls as directed on package. Cool completely, about 10 minutes.
With serrated knife, cut each roll in half crosswise. Spread bottom half of each roll with 1 tablespoon cheese. Top each with 2 spinach leaves; arrange tomato slices over spinach. Add beef, folding to fit roll. Cover with top halves of rolls. Serve immediately, or wrap each sandwich tightly in plastic wrap and refrigerate until serving time.