Heat broiler to high. Place jalapenos, cut side down, on a foil-lined baking sheet and broil until totally blackened, about 10-15 minutes. Cover with the foil immediately upon removing from the oven and let sit for 5 minutes.
Remove the skin from the jalapenos and finely chop the flesh. Set aside.
Meanwhile, place 2 1/2 cups beans in a large bowl and mash until smooth. In a separate bowl, whisk together the eggs, 1 tbsp oil, cumin, salt and cayenne. Stir together the egg mixture, remaining beans, panko, bell pepper, cilantro and shallot. Mix into the mashed beans.
In a small bowl, whisk together the jalapenos and cream cheese.
Form the burger mix into 6 patties. Divide the cream cheese mixture among the patties and stuff inside them so that the black bean mixture completely surrounds them.
Heat 2 tbsp olive oil in a 12-inch nonstick skillet over medium heat until shimmering. Place 3 patties in the skillet. Cook until browned on both sides, about 4-5 minutes per side. Repeat with remaining oil and patties.
Serve warm topped with cheddar cheese on a toasted bun.