First, prepare the toppings. For the Pickled Onions, combine the sliced red onion, lime juice, rice vinegar, salt, and pepper in a small bowl.
Cover and chill for at least 2 hours. For the Lime Mayonnaise, whisk together the mayonnaise, lime zest, and lime juice in another small bowl.
Cover and chill until ready to serve.
In a medium saucepan, heat 2 tablespoons (30 ml / 1 fl oz) of olive oil over medium heat.
Add 1/2 cup (480 ml) of the chopped onion and cook for about 5 minutes, until tender.
Stir in the cracked wheat and water.
Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for about 10 minutes or until all the water is absorbed.
Transfer the cooked wheat mixture to a medium bowl and stir in the soy sauce.
Set aside to cool slightly.
In a food processor, combine the rinsed pinto beans, toasted walnuts, the remaining 1/2 cup (480 ml) of onion, cilantro, minced garlic, cumin, and cayenne pepper. Pulse with several on/off turns until the mixture is well combined but still has some coarse texture.
Add the bean mixture and the soft bread crumbs to the bowl with the cracked wheat.
Stir everything together until just combined, being careful not to overmix.
Divide and shape the mixture into six 3/4-inch-thick patties.
Place the patties on a tray, then brush both sides of each patty with the remaining 2 tablespoons (30 ml / 1 fl oz) of olive oil.
Cover and chill for at least 1 1/2 hours to help them firm up.
Preheat your grill to medium heat. For a charcoal grill, place patties on the rack directly over medium coals. For a gas grill, place patties on the grill rack over the heat.
Grill for 8 minutes total, turning once halfway through, until heated through and nicely marked.
Serve the grilled patties open-face on the toasted bagel tops.
Spread a generous layer of Lime Mayonnaise on each patty, then top with a spoonful of the drained Pickled Onions.
Don't skip the chilling time! It's essential for helping the patties firm up so they don't fall apart on the grill.
