Cut Smokie lengthwise in half, being careful to not cut through to opposite side.
Heat oil in nonstick skillet on medium heat. Add pepper and Smokie, cut sides down; cook 2 to 3 min. on each side or until Smokie is heated through and pepper is lightly browned, occasionally pressing pepper with back of spatula to flatten.
Spread cut sides of bun with mustard. Place Smokie and pepper on bottom half of bun.
Add egg to same skillet; cook 2 min. or until white is set and yolk is cooked to desired doneness. Add to sandwich; cover with Singles and top of bun.