Preheat oven to broil.
Toss tomatoes, onion, and jalapeños with 2 table- spoons vegetable oil in a large bowl. Spread on a baking sheet, cut sides down, and season with salt and pepper. Broil until skins begin to turn dark brown, 6–8 minutes. Remove charred skins and pulse in a food processor to make a chunky sauce.
Heat remaining oil in a large skillet over medium- high heat. Add oregano, red pepper akes, and garlic and then cook until fragrant. Add sauce to skillet and bring to a boil. Reduce heat to medium low and crack eggs into sauce, one at a time. Cook until eggs are desired doneness and season with salt and pepper.
Mash beans with a potato masher or fork, until chunky, then stir in butter until melted.
Assemble burritos by spooning beans on tortillas. Add 1 egg and sauce. Sprinkle with queso fresco and cilantro. Roll burritos as desired.