To make the pico de gallo, combine tomato, onion, jalapeños, lime juice, olive oil, cilantro, salt, and pepper in a medium bowl. Stir, cover, and set aside at room temperature for up to 30 minutes, or refrigerate for up to 3 hours to allow flavors to blend.
To make the burgers, rinse black beans in a colander and set aside. Meanwhile, coat a medium skillet with cooking spray and heat to medium-low. Add red onion and cook, stirring occasionally, about 5 minutes, or until soft. Add garlic and cook, stirring constantly, 2 minutes more.
In a large bowl, combine black beans, onion mixture, panko, cumin, oregano, salt, and pepper. Mash, allowing some chunks to remain. Form bean mixture into four patties about 3 inches wide and half an inch thick.
Divide tortillas into two stacks of four and wrap each stack loosely with foil. Place burgers and tortilla packets on a lightly oiled grill and cook for 4 minutes. Flip burgers and packets and cook for 3 minutes more, or until burgers are lightly browned. To serve, arrange two tortillas on each of four plates. Top with a burger, salsa, and avocado slices and serve.