Place asparagus in a microwave-safe 9-inch pie plate or shallow baking dish with 2 tablespoons water; cover with vented plastic wrap. Microcook on high (100 percent power) for 3 minutes; drain and set aside.
Spread bottom halves of rolls with mustard. Top with cheese, asparagus, ham, turkey, and pickle slices. Add roll tops. Heat oil in a very large skillet or grill pan over medium heat (or preheat a covered electric indoor grill and brush with oil). Place sandwiches in skillet or grill pan or on electric grill (may need to cook in batches); cover sandwiches in skillet or grill pan with a large heavy plate and press gently (or close electric grill lid). Cook for 2 to 3 minutes per side (3 to 4 minutes total in covered grill) or until bread is toasted and cheese is melted. Makes 4 sandwiches.