Preheat oven to 250º F. Place a rimmed sheet pan nearby for transferring the quesadillas. Drizzle olive oil into a medium skillet over medium heat. Add one tortilla and top with about 1/2 cup of pulled pork, 1/2 cup of cheese and onions and jalapenos. Drizzle with prepared BBQ sauce, recipe follows, and top with second tortilla. Carefully flip quesadilla to cook the top side once the bottom tortilla has lightly browned and the cheese is slightly melted. Remove from the skillet and transfer to the rimmed sheet pan. Place into the oven to keep warm as you prepare the rest of the quesadillas.
For the BBQ sauce:
Add all ingredients to a small saucepan over medium-low heat. Stir until well combined and frequently while the sauce cooks. Cook until thickened, about 5 to 10 minutes. Remove from heat.