Make the burger salt Stir together black pepper, kosher salt, and MSG in a small bowl; set aside.

Make the special sauce Combine mayonnaise, garlic, vinegar, paprika, mustard, kosher salt, MSG, and egg, if using, in a blender. Process until smooth, about 1 minute. Transfer mixture to a medium bowl; stir in cornichons. Cover and refrigerate until ready to use.

Make the soubise onions Toss together onions, sugar, and salt in a medium saucepan to coat. Let stand at room temperature 30 minutes. Add butter, and cook over medium, stirring occasionally, until onions are softened and translucent but not browned, 25 to 30 minutes. Remove from heat, and set aside.

Make the smash burgers Shape meat into 8 (4-ounce) balls (about ½ cup each). Heat a large cast-iron skillet or griddle over medium-high. Working in batches, place meat balls in skillet, spacing at least 3 inches apart. Lightly coat the back of a heavy metal spatula with cooking spray, and smash each ball to flatten to about ⅓-inch thickness. (Alternatively, place a small sheet of parchment paper on each meat ball, and smash using a cast-iron burger press; remove parchment.) Sprinkle top of each flattened patty with ¼ teaspoon reserved burger salt. Cook until bottoms are browned and lightly crisp, about 2 minutes. Flip patties, and sprinkle each with ¼ teaspoon burger salt. Reserve remaining burger salt for another use (see Note). Top each patty with 1 cheese slice. Cook until cheese is melted and patties are cooked through, about 2 minutes.

Place 2 tablespoons reserved soubise onions on each bottom bun. Top each with 2 patties, 1 ½ tablespoons special sauce, and 4 to 5 pickle slices. Cover with top buns. Reserve remaining soubise onions and special sauce for another use (see Note). Serve immediately.