Melt the butter in a frying pan over high heat. Add the mushrooms and leek and cook for 2–3 minutes, stirring frequently, until they soften considerably. Toss in the jalapeño, sugar, and garlic and continue stir-frying for another 2–3 minutes until fragrant. Add the beans to the pan and cook for 1 minute, stirring to combine everything well.
Remove the pan from the heat and season the mixture generously with salt and pepper. Using a potato masher, mash the bean mixture until it breaks down into a rough, chunky texture with no large lumps remaining. You want it cohesive enough to hold together but still with some texture. Divide the mixture into 6 equal portions and shape each one into a burger patty with your hands.
Spread some flour onto a plate and season it well with salt and pepper. Gently coat both sides of each burger patty in the seasoned flour, tapping off any excess. This creates a nice crust when cooking.
Heat the oil in a clean frying pan over medium-high heat. Add the floured burgers to the hot pan and cook for about 3–4 minutes on each side until they develop a golden brown crust and are heated through completely.
While the burgers are cooking, prepare the dressed lettuce by whisking together the mayonnaise, mustard, and lemon juice in a bowl until smooth. Add the shredded lettuce and diced onion, tossing until everything is evenly coated in the creamy dressing.
Serve the hot bean burgers in toasted buns, topped with the dressed lettuce and some fresh red onion slices for added crunch and flavor.
