Smoked Gouda and Caramelized Onion Quesadillas

6 tablespoons butter, divided

1 large onion, thinly sliced

2 tablespoons golden brown sugar

1 teaspoon white wine vinegar

1½ cups grated smoked Gouda cheese

4 flour tortillas, 10-inch size

2 ounces thinly sliced prosciutto, chopped

Melt 2 tablespoons butter in heavy medium skillet over medium heat. Add onion, brown sugar, and vinegar; saute until onion is golden brown, stirring frequently, about 25 minutes. Remove from heat and cool to room temperature.Heat oven to 350.Melt the remaining butter.Sprinkle cheese over half of each tortilla, dividing equally. Sprinkle prosciutto and sauteed onion over cheese; season with pepper. Fold other half of each tortilla over cheese mixture. Brush tortilla with some of the melted butter.Brush heavy large skillet or griddle pan with some of the melted butter and place over medium-high heat. Working in batches, cook quesadillas just until brown spots appear, brushing skillet with butter between batches, about 2 minutes on each side. Transfer quesadillas to heavy large baking sheet.Bake until tortillas are golden and cheese melts, about 5 minutes.Transfer quesadillas to work surface. Cut each into 4 triangles. Arrange on platter and serve hot.Serves four.