Heat oven to 350°F; line a 9-by-13-inch pan with parchment.

Toss pork with barbecue sauce until coated, not soupy.

Slice rolls horizontally as one slab; place bottom in pan.

Layer half the cheddar, pork, drained pickles, and remaining cheddar. Replace top slab.

Mix butter, smoked paprika, and garlic powder; brush rolls.

Cover; bake 18 minutes. Uncover; bake 5 to 7 minutes until filling reaches 165°F. Rest; cut into 12.