In a small bowl, combine mayonnaise, lime juice, garlic powder, and a pinch of salt. Mix until smooth and refrigerate.
Finely dice the jalapeños, removing the seeds if you prefer a milder flavor.
Divide the ground beef into four equal portions and gently shape each into a loose ball.
Heat a cast iron skillet or heavy griddle over medium-high heat until very hot.
Butter the cut sides of the buns and toast until golden brown.
Place one beef ball onto the hot skillet and firmly press it into a thin patty using a sturdy spatula. Season immediately with salt and pepper.
Cook for 2–3 minutes until the edges become crisp and browned.
Flip the patty, top with pepper jack cheese and diced jalapeños, then cook another 2 minutes until the cheese melts.
Repeat with the remaining patties.
Spread the chilled jalapeño mayo on both toasted buns. Assemble each Jalapeño Popper Smash Burgers with the cheesy patty and your preferred toppings. Serve immediately.