Preheat oven to 450 degrees. Set jalapenos on a baking sheet and roast 15-20 minutes, turning two or three times, until charred all over. Remove from the oven and place in a plastic storage bag. Seal and let the jalapenos sweat while you prepare other components of the dish.
In the bowl of a food processor or high speed blender, whip together black beans, panko, garlic, egg, chili powder, cumin, Worcestershire, soy sauce, and a pinch of salt and pepper. With a spatula, stir in flour one tablespoon at a time until a sticky but cohesive mixture forms. You may need up to 6 tbsp but do not exceed this amount. Pour batter into an airtight container and set in the fridge at least 20 minutes. The chilling time will help set the batter.
Meanwhile, make the salsa. Combine corn, tomato, red onion, cilantro, lime juice, and salt. Cover and chill in the fridge until ready to serve.
Remove burger batter from the fridge and let it sit at room temperature while you prepare the jalapeno popper filling. Peel the skin off the jalapenos and remove the cap. Slit in half and scrape out the seeds, then dice into small pieces. In a bowl, stir together cream cheese, jalapenos, cheddar cheese, and chives. Taste for salt and pepper.
Form four patties out of half of the black bean batter. The batter may still be sticky, but that's okay! They will set beautifully when cooked. Spoon about 2 tbsp jalapeno popper filling to each burger. Pat the remaining batter into four patties and set atop the filling. Pinch the two layers of burger together to seal the filling.
Line a plate with paper towels. Heat 1/4 cup olive or avocado oil in a large skillet over medium heat. Set burgers with about 1/2 inch space between them - you may need to do two batches - and cook 5 minutes per side, flipping once. Cover the skillet with a lid and cook an additional 3-4 minutes to set the inside of the burger. Move burgers to the paper towel lined plate to drain.
Slice four burger buns in half. Toast under the broiler for 3-4 minutes if desired. Add a tuft of greens to the bottom bun, then slide a burger overtop. Sprinkle with tomato corn salsa.