Stuff four hamburger patties with 15 ml (1 tablespoon) jalapeño pesto each. Season with salt and pepper. Preheat the grill, setting the burners on medium-high. Oil the grate. Grill the patties for 4 to 5 minutes on each side or until cooked through.
Toast the hamburger buns. Spread the inside with Dijon mustard and mayonnaise. Layer with lettuce leaves and the patties. Add, to taste, slices of cheese, tomato, sandwich pickles, and onion.