Line a baking sheet with parchment paper and preheat the oven to 400 degrees F. Heat a large skillet over medium-high heat. Add the olive oil, onion slices, garlic, 1/4 teaspoon salt and 1/8 teaspoon pepper and cook, stirring occasionally, until the onions are softened, about 10 minutes. Reduce the heat to medium-low and cook until golden, about 10 minutes more.
Using a blender, puree together 1/4 cup of the caramelized onions, sour cream, soy sauce and, if necessary, 1 tablespoon water for a dip consistency. Transfer to a bowl. Stir in 1/4 cup of the caramelized onions and season with salt and pepper.
Meanwhile, arrange the mushroom caps on the lined baking sheet, stem-sides down, and bake, 10 minutes. Flip the mushroom caps over, draining any liquid, and mound the dip into each one. Sprinkle evenly with the cereal crumbs and bake until the mushrooms are tender and the tops are golden, about 20 minutes. Top with the remaining caramelized onions and serve.