12 oz. shiitake mushrooms
7 oz. smoked or firm tofu drained, cut into 1 “-2” pieces
1 medium onion, cut into a few large pieces
¼ cup plus 3 Tbsp. vegetable oil
5 garlic cloves, finely chopped
¼ cup gochujang (Korean hot pepper paste)
1 tsp. five-spice powder
½ tsp. ground cumin
3 Tbsp. Shaoxing wine or medium-dry sherry
2 Tbsp. vegetarian mushroom oyster sauce
2 Tbsp. vegetable oil
1 tsp. toasted sesame oil
6 English muffins, split or Sesame Buns
2 green onions, thinly sliced
½ cup coarsely chopped cilantro
1 Tbsp. toasted sesame seeds
Working in batches, pulse button and shiitake mushrooms in a food processor until finely chopped. Transfer to a medium bowl.
Working in batches, pulse tofu in food processor until pea-size. Transfer to a small bowl.
Pulse onion in food processor until very finely chopped. Transfer to another small bowl.
Heat ¼ cup oil in a large pot over medium. Cook mushrooms, stirring occasionally, until browned and shrunken by about one third, 8-10 minutes. Transfer mushrooms back to their bowl. Wipe out pot.
Heat remaining 3 Tbsp. oil in pot over medium. Add onion and garlic and cook, stirring occasionally, until onion is tender and browned around the edges, 8-10 minutes.
Add gochujang, five-spice, cumin, and tofu to pot and cook, stirring, until tofu and onion are coated, about 2 minutes. Pour in wine and cook just until alcohol smell has burned off, about 1 minute. Add oyster sauce and 4 cups water and return mushrooms to pot. Partially cover pot and cook mushroom mixture until mixture is thickened and very soft and silky, 50-65 minutes. Remove from heat and season with salt.
Whisk vegetable oil and sesame oil in a small bowl to combine, then brush cut sides of each English muffin with oil mixture.
Heat a large nonstick skillet over medium-high. Cook English muffins, cut sides down, until golden brown underneath, about 1 minute. Transfer to plates, arranging cut side up.
Spoon some mushroom mixture onto bottom halves of English muffins or Sesame buns and top with green onions, cilantro, and sesame seeds.