In a large-bowl, combine ground-beef, jalapeno, garlic, chili-powder and season with pepper and salt. Mix until just blended, then form mixture into 4 thin patties.
In a large-skillet over medium-high warmth, heat 1 tbsp of oil. Cook patties for your preferred doneness, about 4minutes each side for medium. Transfer to a plate and then wipe skillet clean.
Heat 1 tbsp oil over moderate heat. Insert a flour-tortilla and top with a small handful all lettuce and cheeses.
Put a cooked burger at the top, then top with cheese, cup pico-de-gallo & a spoonful of sour-cream. Top with a tortilla & cook until golden, about a few minutes.
Flip quesadilla & cook two minutes or longer. Repeat with remaining ingredients to create 4 quesadilla-burgers.