Note: Roasted chicken (plain, lemon or honey-flavored varieties) bought at a local market works well. Shred the chicken into small pieces to make 1 cup.
2 tbsp. unsalted butter
1½ lb. onions, sliced
1 tsp. sugar
1½ tsp. salt
Scant ¼ tsp. red pepper flakes
8 (6-to 7-inch) flour tortillas
2 2/3 c. shredded Monterey Jack cheese
1 c. cooked roasted chicken, shredded into small pieces (see Note)
2 tsp. grated lime zest (color portion of peel)
4 tsp. lime juice
5 tbsp. chopped cilantro
Oil for grilling or sautéing
Recipe
Melt butter in large heavy skillet set over medium heat. When hot, add onions and cook, stirring often, 1 minute. Add sugar and salt and continue to cook, stirring, until onions are soft and well browned, 15 to 20 minutes. Remove from heat. Stir in red pepper flakes. Set aside.
Place tortillas on work surface. Sprinkle 1/3 cup cheese over each tortilla. Divide onions and spread evenly over cheese layer. Top with shredded chicken. Sprinkle ¼ teaspoon lime zest and ½ teaspoon lime juice over each tortilla. Finally, sprinkle ½ tablespoon cilantro over each. Fold tortillas in half to form half-moon shapes.
(Tortillas can be prepared 30 minutes ahead. Cover with slightly dampened kitchen towel and leave at cool room temperature.)
If you have a stove-top grill pan, lightly coat with oil. If not, coat bottom of large skillet with oil. Place pan over medium-high heat and, when hot, add enough quesadillas to fit comfortably in single layer. Cook until golden brown outside and cheese has melted inside, 2 minutes or less per side. Remove, cover loosely with foil and finish cooking the rest.
With sharp knife, cut each cooked quesadillas into 2 equal triangles. Arrange in overlapping rows on heated serving platter. Sprinkle with remaining cilantro.