Preheat the oven to 450 degrees F. Place the mushroom caps on a baking sheet. Mix the adobo seasoning, 1/4 teaspoon salt and a few grinds of pepper in a small bowl. Drizzle the mushroom caps on both sides with the vegetable oil and sprinkle with the adobo mixture. Roast until tender and flattened, flipping halfway through, 20 to 25 minutes. Let cool about 5 minutes on the pan.
Meanwhile, heat the refried beans in the microwave for about 1 minute; stir until smooth. Combine the avocado, pickled jalapeños and brine in a medium bowl; roughly mash with a fork.
Heat 1/4 inch vegetable oil in a large skillet over medium heat. Mix the egg and 1 tablespoon chipotle mayonnaise in a medium bowl with a fork. Add the panko to another medium bowl. Pat the mushroom caps with a paper towel to remove the excess moisture, then dip in the egg mixture and then the panko to coat. Fry until golden brown, 2 to 3 minutes per side, reducing the heat if browning too quickly. Drain on a paper towel–lined plate.
Assemble the sandwiches: Spread 1 tablespoon chipotle mayonnaise on each roll bottom, then top with a layer of mashed avocado, a fried mushroom cap and a handful of shredded lettuce. Spread the refried beans and pico de gallo on the roll tops, then set into place. Cut the tortas in half before serving.
