Remove stems from Portobellos; slice each cap into 6 cubes. Place those cubes into a large bowl.
In a small bowl, combine the mirin, sherry, and 1 tablespoon olive oil; drizzle over the mushrooms. Using your hands, gently coat and toss the mushrooms with the mirin mixture. Set aside and let marinate for about 20-30 minutes.
While the portobellos cubes are marinating, preheat the broiler to high.
Heat the olive oil in a large sauté pan and add onion slices. Cook onions for 5 - 7 minutes and add the sugar and stir to combine. Cook another 5 minutes until the onions brown and caramelize.
To make the tangy hoisin sauce, whisk together the hoisin, tamari, Worcestershire, dried ginger, and water.
Add the bread crumbs to the bowl of mushrooms and coat thoroughly. Line a baking sheet with foil and lightly spray with cooking spray. Add the marinated mushrooms and place directly under the broiler for 10 minutes. Use tongs to turn the mushrooms and pour any extra sauce over them. Then return the pan to the oven and cook for another 10 minutes.
To assemble the sandwiches, spread some hoisin sauce on the bottom bun, then top with several crispy Portobello pieces. Top with grilled onions, more sauce, and some fresh cilantro leaves. Top with top bun piece.
Notes
If you don't have access to mirin, you can sub with a sweet white wine.Note: Nutrition information does not include sourdough buns.