Cook the onions. Heat a large cast-iron skillet over medium heat. Slice the onion into thin half-moons. Add 2 tablespoons oil to coat the bottom of the pan. Add the onions, season with the salt and pepper, and stir to coat. Cook for about 5 minutes, stirring occasionally, until softened and lightly caramelized, golden on the edges but still with some crunch. Transfer to a plate and turn off the heat, but don't clean the pan.
While the onions cook, make the smash dough. Drain the lentils well so there’s very little extra liquid. In a blender, puree the lentils, vegetable broth, miso, and oil until the mixture resembles hummus.
Transfer to a large bowl and add the vital wheat gluten, breadcrumbs, onion powder, smoked paprika, and garlic powder. Knead until a pliable, gluten-y dough forms, about 2 minutes.
Divide the dough in half. If you're not making the full recipe, wrap one half and refrigerate for later. Divide the remaining dough into 4 pieces. On a cutting board or clean counter, roll each piece with a rolling pin into a thin disc about 6 inches across. The edges should be scraggly and uneven, not a tidy circle.
Heat the cast-iron pan over medium heat. If it isn't gigantic, cook 2 or 3 burgers at a time so they have room to smash.
Drizzle in oil to cover the bottom of the pan. Add the patties and squish them down with a metal spatula. Cover and cook for about 4 minutes, until seared. Smash again, drizzle the tops with oil, and flip, smashing the other side. Cover and cook for about another 4 minutes, until cooked through but tender inside, not mushy.
Stack the burgers up in the pan and add the onions back in 4 piles. Place the burgers on top of the onions, smash them in, and lay the cheese on top. Raise the heat a little, add ¼ cup water right to the center of the pan, cover, and steam for a minute or so to melt the cheese.
Assemble. For singles, spread a little burger sauce on the bun and add lettuce. Lift the onions and burger onto the bottom bun with a spatula. Follow with tomato and a few pickle slices, drizzle with more burger sauce, and finish with the top bun. Repeat with the remaining ingredients. For doubles, stack a second layer of burger and onions before adding the tomato and pickle. Serve immediately.
