COMBINE eggs, salt and pepper in small bowl; set aside.
MELT 2 teaspoons butter in large, nonstick skillet over medium-high heat. Pour in egg mixture. Cook eggs by carefully pushing cooked portions at edges toward center until set; remove from heat.
SPREAD pesto evenly over bottom roll halves. Layer with cooked eggs, tomato, basil and cheese. Top with roll tops; secure with wooden picks.
MELT remaining 2 teaspoons butter in large, nonstick skillet over medium heat. Place sandwiches in skillet and cook, pressing frequently with the back of a spatula, for 4 to 5 minutes or until bottoms are golden brown. Carefully turn sandwiches over; continue to cook until top sides are golden brown and cheese is melted.
REMOVE wooden picks; cut in half and serve immediately.