Toss together the Cheddar, Monterey Jack and pepper jack in a bowl; set aside.
Heat 2 tablespoons of the butter in large skillet over medium heat. Place a single tortilla in the skillet. Sprinkle a little less than a third of the cheese blend over the tortilla. Sprinkle with salt and pepper. Add about a third of the diced tomato and a third of the chiles. Sprinkle a touch more cheese over the whole thing and gently top and press with a second tortilla. Cook until golden on the bottom, about 3 minutes.
Carefully flip the quesadilla to the other side. Continue cooking until the second side is golden, 3 to 4 minutes more. Repeat with the remaining ingredients. Slice each quesadilla into wedges and garnish with cilantro sprigs.