Prep the Sweet Potatoes: Place the grated sweet potatoes in a clean kitchen towel and squeeze out as much excess moisture as possible (this is key for crispy buns).
Make Bun Batter: In a medium bowl, combine the grated sweet potatoes, beaten eggs, garlic powder, onion powder, and salt.
Cook the Buns: Lightly grease and preheat a waffle maker or a large skillet over medium heat. Scoop about ½ cup of the mixture per bun and press down firmly. Cook until golden and crispy on both sides (about 5–8 minutes). Repeat to make 8 buns total.
Mix the Sauce: In a small bowl, whisk together the mayonnaise, Greek yogurt, ketchup, yellow mustard, and pickle juice until smooth.
Cook Smash Patties: Divide ground beef into 4 equal balls and season generously with salt and pepper. Heat a cast-iron skillet over high heat. Place beef balls into the screaming-hot skillet one at a time and smash them very thin immediately using a sturdy spatula. Sear for 2–3 minutes per side until deeply browned and edges are crispy.
Melt Cheese: Place a cheese slice onto each patty right after flipping; cook until fully melted.
Assemble: Layer a bottom sweet potato bun with burger sauce, cheesy smash patty, tomato slice, crisp romaine lettuce, an extra spoonful of sauce, and top with the second sweet potato bun. Serve warm.