Preheat oven to 450 degrees. Wash and dry all produce. Thinly slice jalapeño, removing ribs and seeds if you prefer less heat. Core, deseed, and thinly slice green pepper. Halve, peel, and thinly slice onion. Halve lime.
In a small bowl, combine jalapeño, juice from half the lime, ¼ tsp sugar and a pinch of salt. Stir until sugar and salt have dissolved; set aside to quickpickle. In a separate small bowl, combine BBQ sauce and 2 TBSP ketchup.
Place flatbreads on a baking sheet and top with a drizzle of olive oil. Season with salt and pepper. Toast in oven until lightly browned, 5-7 minutes.
While flatbreads toast, heat a drizzle of olive oil in large pan over medium-high heat. Add green pepper and a pinch of salt and pepper. Cook, stirring, until slightly softened, 3-4 minutes. Add onion and another drizzle of olive oil; season with salt and pepper. Cook, stirring, until softened and lightly charred, 5-6 minutes. Turn off heat.
Evenly spread toasted flatbreads with BBQ sauce mixture. Sprinkle with pepper jack, Monterey Jack, and veggies. Bake until cheese is melted and edges are crispy, 5-7 minutes.
Top baked flatbreads with as much pickled jalapeño as you’d like. Cut into equal-sized pieces and divide between plates.