Special equipment: a deep-frying thermometer
Heat 2 inches of vegetable oil in a heavy-bottomed pot to 350 degrees F.
Put the flour in one shallow dish, the egg in a second and the breadcrumbs in a third. Coat the onion rings first in the flour, then dip them into the egg, shaking off any excess, then coat them with the breadcrumbs. Fry the rings until golden brown, 2 to 3 minutes. Drain on a paper towel-lined plate and set aside.
Put the ground sirloin in a bowl and add the chipotle and some salt and pepper. Mix well and form the mixture into 2 burgers.
Heat a cast-iron skillet over medium-low heat and add the olive oil. Cook the burgers to your liking, 10 to 15 minutes. Set aside on a plate and keep warm by inverting another plate on top. In the same skillet, fry the jalapeno slices until lightly browned, 2 to 3 minutes. Wipe out the skillet and add the butter. Toast the pretzel rolls until lightly browned.
Mix together the barbecue sauce and mayonnaise in a small bowl.
To assemble: Spread some of the sauce on the bottom halves of the rolls. Top with the burgers, jalapeno slices and onion rings. Spread more sauce on the top halves of the rolls and serve.