Whisk together the vegan mayo, ketchup, yellow mustard, sweet pickle relish, garlic powder, smoked paprika, salt, black pepper, and apple cider vinegar in a small bowl until smooth and well combined. Set aside. This sauce should be made first so the flavors can meld while you prepare the patties.

Rinse and thoroughly dry the black beans, then mash them in a large bowl until mostly broken down but still slightly chunky—this texture creates a better binding structure. Add the cooked lentils, oat flour, panko breadcrumbs, soy sauce, nutritional yeast, tomato paste, garlic powder, smoked paprika, sea salt, onion powder, black pepper, and liquid smoke. Mix everything together by hand until well combined and cohesive. I find that mixing by hand helps me feel when the texture is right and ensures the ingredients are evenly distributed without overmixing.

Divide the patty mixture into 4 equal portions and gently form each into a ball—don't compress them too tightly or they'll be dense. While you're forming the balls, prepare all your burger toppings: thinly slice the red onion, slice the beefsteak tomato into rounds, separate the butter lettuce leaves, and place the dill pickle chips in a small bowl. This mise en place approach means you won't be scrambling while the patties are cooking.

Heat the avocado oil in a large skillet over medium-high heat until it shimmers and a drop of water sizzles on contact—this indicates it's ready for the smash. Place a patty ball in the center of the pan and immediately press it down firmly with a spatula to about 1/4-inch thickness, creating a thin, wide patty that will develop a crispy crust. Let it cook undisturbed for 3 minutes without moving it—this is crucial for building that golden, flavorful crust that makes smash burgers special. I like to listen for the sizzle to quiet down slightly, which tells me the crust has set.

Carefully flip each patty, then immediately place a slice of vegan cheddar cheese on top of the hot patty. Cook for another 3 minutes, allowing the cheese to melt and the bottom side to develop its own golden crust. You can cover the skillet with a lid or tent it with foil if you want the cheese to melt faster, but it's not necessary. Repeat the smashing and cooking process with the remaining patty balls in batches as needed.

While the last patty is cooking, lightly toast the brioche-style vegan buns to add texture and prevent them from getting soggy. Spread a generous amount of the special sauce from Step 1 on both the top and bottom buns. Place a cheese-topped patty on the bottom bun, then layer with butter lettuce, tomato slices, red onion slices, and dill pickle chips. Top with the upper bun and serve immediately while the patties are still warm.