Make the aioli by adding the egg yolks and Dijon mustard to a food processor. Blend briefly, then slowly stream in the oil while the processor runs until the mixture is thick, glossy, and fully emulsified.
Make the jalapeño cheese spread by adding the cheddar curds, pickled jalapeños, garlic powder, and dried scallions to a food processor. Pulse until the mixture is chunky and spreadable, not smooth. Season with salt, black pepper, and a pinch of citric acid if you want a brighter flavor.
Portion the ground beef into 4-ounce balls. Keep the meat loose and do not overwork it so the smash burgers stay tender.
Heat a flat top or cast iron skillet over high heat. Place a beef ball on the hot surface, cover with parchment paper, and smash as thin as possible. Remove the parchment right away, then top with thinly sliced leeks, salt, and black pepper.
Cook the smash burger until a deep crust forms on the bottom. Flip once, then top with pepper jack cheese. Cover with a bowl or lid for 30 to 60 seconds to help the cheese melt.
Toast the burger buns until golden. Spread the jalapeño cheese mixture on the bottom bun, then layer with one patty, more cheese spread, the second patty, more cheese spread, and the top bun.
Serve immediately while the smash burgers are hot, crispy, and the cheese is fully melted.