Lay 2 tortillas on the work surface. Distribute the cheese evenly between the 2 tortillas. Arrange the sliced tomatoes over the cheese. Sprinkle the scallions and cilantro on top of the tomatoes. Place the remaining tortillas on top of each of the filled tortillas.
Coat the interior of a large saute pan with clarified butter. Gently place 1 quesadilla in the pan. Brush the top with clarified butter. Cook over medium heat until the underside is golden brown. Using 2 spatulas, flip the quesadilla. Cook until golden brown. Cut into 6 pieces. Serve with Tomatillo Salsa.
Preheat the broiler. Place the tomatillos on a baking sheet and broil until they begin to blacken. When the tomatillos are cool, place them in a blender with the jalapenos, lime juice, sugar and salt. Puree. Add to remaining ingredients and mix well.