Special equipment: a ring mold; a deep-fry thermometer
1. Heat 2 tablespoons of the oil in a large saute pan over high heat until it begins to shimmer. Add the mushrooms and let sit for at least 3 minutes without touching. Stir and let sit again until mushrooms begin to brown and water begins to evaporate. Cook until golden brown and dry. Season with salt and pepper. Add the barbecue sauce and a splash of water and cook until the mushrooms are glazed, about 2 minutes. Transfer to a baking sheet and let cool to room temperature.
2. Combine the mushrooms, Quinoa and Chickpea Puree in a bowl. Mix in the cilantro. Taste for seasoning, adding more salt and pepper if needed. (Remember that the quinoa was seasoned with salt, the mushrooms were seasoned with salt and pepper and the egg wash and quinoa flour will be seasoned). Cover the mixture and refrigerate until chilled, at least 2 hours.
3. Heat 2 inches of oil in a medium high-sided saute pan over high heat until it registers 350 degrees F on a deep-fry thermometer.
4. Form the burgers (using a ring mold) into 4 burgers (I got 4 burgers that were each about 4 1/8 ounces).
5. Whisk together the eggs in a shallow bowl and season with salt and pepper. Put the quinoa flour in a shallow bowl and season with salt and pepper.
6. Using a fish spatula, gently put a patty into the egg wash; remove and let the excess drip off. Dredge the patty in the flour and tap off the excess. Repeat with the remaining patties.
7. Fry the patties until golden brown and crisp, about 3 minutes, flipping halfway through the cooking process. Remove to a plate lined with paper towels.
8. Heat the remaining 1 tablespoon oil in a large nonstick pan over high heat until it shimmers. Add the patties and top each with a slice of cheese. Remove from the heat and slowly add 1/4 cup of water to the pan (careful not to hit the burger). Cover, return to the heat and count to 10. Remove the lid, the cheese will be melted.
9. Place the burgers on the bottoms of the buns, top with a large dollop of Green Onion-Mustard Slaw and drizzle with some of the reserved mustard dressing.
Combine the salt with 1 cup of water in a medium saucepan and bring to a boil over high heat. Stir in the quinoa, bring to another boil, reduce the heat to medium-low, cover and cook until tender and the water is absorbed, about 25 minutes. Remove from the heat, let sit for 10 minutes and fluff with a fork. Spread evenly onto a baking sheet and let cool completely. The quinoa can be made a day ahead and stored in a container with a tight lid.
1. Drain the chickpeas in a colander. Rinse and drain again. Line a baking sheet with paper towels and drain the chickpeas for at least 15 minutes.
2. Transfer the chickpeas to a food processor and process until coarsely chopped. Transfer to a bowl.
1. Whisk together the vinegar, honey, mustards and sugar in a medium bowl until smooth.
2. Combine both cabbages and both onions in a large bowl. Add 1/2 cup of the dressing and toss to combine. Season the slaw with salt and pepper and let sit at room temperature for at least 30 minutes to allow the flavors to meld and the cabbage to wilt. The slaw can be made 4 hours in advance and stored covered in the refrigerator. Reserve the remaining dressing for the burger.