Heat oven to 350°F. Slice a lid from each roll and pull a little soft bread from the bottoms, leaving walls about 1/2 inch thick; reserve removed bread for another use.

Melt butter in a skillet over medium heat. Add ham and cook for 4 to 5 minutes, then add spinach and cook for 3 to 4 minutes until wilted and the pan is dry.

Stir in cream cheese, half the smoked cheddar, mustard and pepper. Heat the filling to 165°F, stirring until creamy.

Divide filling among the roll bottoms on a sheet pan and top with remaining cheddar. Bake for 10 to 15 minutes until the centers reach 165°F and cheese melts, adding the roll lids cut side up for the final 3 minutes.

Set the lids over the filling, rest for 2 minutes and serve one closed hot roll per person.