Preheat a large stovetop grill pan or a large, nonstick skillet over medium-high heat.
Working with 2 at a time, place sandwiches, oiled side down, and brush tops with half of the remaining oil. Grill 2 ½ to 3 minutes, or until golden brown. Turn and cook another 2 ½ to 3 minutes, until golden brown and sandwich is heated through. Repeat with remaining 2 sandwiches.
Slice sandwiches in half at an angle, and serve warm.
Garnish each half with a dollop of leftover Muhummara spread, and parsley sprig, if desired.