Heat oven to 350°F. Melt 1 tablespoon butter in a skillet over medium-low heat; add eggs. Cook, gently scraping cooked eggs off the bottom creating soft curds, until just cooked through.

Place bottom half of rolls on a lightly sprayed rimmed baking pan. Layer 6 slices cheese, ham, eggs and remaining cheese. Cover with top of rolls.

Mix together 2 tablespoons melted butter, dill and onion powder. Brush butter mixture over top of rolls; cover pan with aluminum foil.

Bake 15 minutes. Uncover and bake 5-8 minutes until cheese is melted and buns are crisp. Cut into individual sandwiches before serving.