Heat a large skillet over medium heat and add 1 tablespoon of olive oil. Add in the leeks, apple and brussels and stir. Add the salt and pepper, stirring well, then cook until the veggies are slightly soft, about 5 to 6 minutes. Add in the balsamic vinegar and stir, cooking for another minute. Remove the veggies from the heat.
Add the veggies to a food processor along with the quinoa, chickpeas and eggs. Pulse until the veggies and beans are in coarse pieces – you don’t want them pureed – and the eggs are combined. Scoop the mixture into a bowl and stir in the flour and smoked paprika until it is combined. Form patties that are about 2 inches wide and almost 1 inch thick – if you try to get them thicker than that, they will probably fall apart. Add the remaining 1 tablespoon of olive oil to the same skillet and heat over medium-high heat. For me, the key to getting veggie burgers to crisp up is to cook them at a slightly higher heat. Add the patties (in batches, if needed) and cook for about 5 minutes per side, until they are golden brown and crisp. Reduce the heat to low, add the havarti slices and cook until the cheese melts.
For the mushrooms, heat a large skillet over medium-low heat and add the olive oil. Add the mushrooms and stir. Cook until the mushrooms are soft, about 8 to 10 minutes, stirring occasionally. Turn off the heat and sprinkle with salt and pepper. Assemble the burgers on the whole wheat buns, adding the mushrooms and then the slaw.