Preheat a panini press. Preheat olive oil in a large skillet over medium-to-high heat. Add onion and cook, stirring, until onions begin to brown, about 8 minutes. Reduce heat to low and continue to cook until onions soften and darken, another 15 minutes. Add jelly and stir to incorporate. Remove from heat and reserve.
Split rolls and spread about 3 tablespoons red pepper jelly on the bottom side of each roll. Layer 4 slices of turkey and 2 slices Swiss cheese on each roll. Spread mustard on top half of each roll. Spray cooking spray on both sides of the panini press. Place 2 sandwiches on the press and toast until browned on each side and cheese is melted, about 7-8 minutes total. Slice in half and serve, or wrap in foil to take on the go.