Wrap each cucumber with plastic wrap. Pound with a rolling pin until cracked and slightly flattened. Remove from plastic and slice cucumbers in half lengthwise, then into 1" sections. Place in colander and toss with salt and sugar. Allow to sit and drain for 15 minutes.
In a bowl combine rice vinegar, sesame seeds, soy sauce, sesame oil, and garlic. Whisk well and add cucumbers. Toss until well coated and allow to sit for at least 10 minutes. Hold refrigerated for service.
In a bowl combine mayonnaise, pickle juice, and gochujang paste. Whisk until well mixed. Hold refrigerated for service.
In a bowl combine cabbage, shredded carrots, and spicy sauce and mix well. Hold refrigerated for service.
In a bowl combine ground beef, scallions, and garlic. Mix until ingredients are evenly distributed. Divide into 4 oz. portions and form gently into balls. Hold refrigerated for service.
Set griddle to medium high. For each serving, place 1 seasoned beef ball on hot griddle and press down with the back of a spatula. Continue to press until burger forms a crust. Flip and cook to desired doneness. Season with salt and pepper. Toast 1 bun.
Spread 1 tablespoon of spicy sauce on both the top and bottom bun. Place smash burger on bottom bun and top with 1/2 cup cabbage mixture, 1/2 cup smashed pickles, and top bun. Serve hot with desired accompaniments.
If baby cucumbers are unavailable use 1 regular sized cucumber and chop into 1 inch (2.5-cm) cubes.