Mix the mayonnaise, lime juice, minced chipotle pepper or adobo sauce, smoked paprika, and a pinch of salt in a small bowl. Cover and refrigerate until the burgers are ready.

Place the ground beef in a large bowl. Add the minced chipotle chiles, adobo sauce, onion, garlic, Worcestershire sauce, smoked paprika, cumin, kosher salt, black pepper, and minced jalapeño if using.

Mix gently with your hands just until the seasonings are distributed. Divide the mixture into four portions of about 6 ounces each, shape them into patties approximately 3/4 inch thick, and press a shallow indentation in the center of each patty.

Refrigerate the patties for 20–30 minutes if time allows. Meanwhile, heat a clean grill to medium-high, approximately 400–450°F, and lightly oil the grates.

Grill the patties for about 4–5 minutes per side, turning once. Cook until the centers reach 160°F for ground beef, and do not press the patties with a spatula.

Place a slice of pepper Jack or cheddar on each patty during the final minute of grilling. Close the lid briefly so the cheese melts, then toast the buns cut-side down for 30–60 seconds.

Spread chipotle-lime mayonnaise over the toasted bun halves. Assemble each burger with the grilled patty, lettuce, tomato, red onion, avocado, pickled jalapeños, or any combination of the suggested toppings, and serve immediately.