Preparation Cook quinoa in a large saucepan of lightly salted boiling water, stirring occasionally, until tender, 8–10 minutes. Drain well and let cool at least 10 minutes. Meanwhile, heat 1/4 cup oil in a large nonstick skillet over medium-high. Add chickpeas (make sure they are well drained) and cook, tossing occasionally, until lightly browned, 8–10 minutes. Add garlic powder and paprika and toss a few times to coat. Transfer to a large bowl and let cool about 5 minutes. Add mushrooms, tahini, miso, and 1/4 cup oil to bowl with chickpeas and mash with a potato masher or fork to combine. Add quinoa and flour and mash until mixture holds together when squeezed in your hand. Taste and season with salt if needed. Form into 8 patties and arrange on a parchment-lined rimmed baking sheet. Freeze until firm, about 2 hours. At this point, the patties can be baked, or they can stay frozen up to 3 months. Transfer to resealable freezer bags or layer in an airtight container with sheets of parchment between patties. Preheat oven to 425°. Drizzle frozen patties generously with oil on both sides on a rimmed baking sheet. Bake patties until browned and crisp, 25–30 minutes. Place a slice of cheese on top of each patty and bake until cheese is melted, about 1 minute. Spread mayonnaise and mustard on cut sides of buns (if using). Place burgers on bottom buns. Top with lettuce and pickles (if using) and close up burgers. Do Ahead: Patties can be made 3 months ahead. Transfer to a resealable freezer bag and freeze.