Combine all the sauce ingredients in a small bowl. Mix thoroughly and set aside to let the flavors develop.
Smash Burgers
Spread the softened butter evenly on the cut sides of the potato buns. Place the buns cut-side down on a griddle or skillet and toast until golden brown. Set aside.
Divide the ground beef into 4 equal portions and form each portion into a loose ball.
Heat a large griddle or cast-iron skillet over high heat. Once it is hot, place a beef ball on the griddle or skillet and immediately smash it with a spatula or burger press until it is very thin. Season generously with salt and pepper. Cook for 1 to 2 minutes until the edges become crispy. Flip the patty and season the other side with salt and pepper. Top the patty with a slice of cheese and cook for another 30 to 45 seconds until the cheese begins to melt. Repeat this process with the remaining patties.
To assemble each burger, spread Smasher sauce on a bottom bun and place it on a plate. Add a cheese-topped patty followed by 4 pickle slices and a tablespoon of onions. Spread additional Smasher sauce on the top bun and place it on the burger. Serve immediately while hot.