Smashed Burgers

Name: Smashed Burgers
Cuisine: American
Ingredients: 2 tablespoons mayonnaise; 1 tablespoon minced shallot; 1.5 teaspoons finely chopped dill pickles; 1/2 teaspoon pickle brine; 1.5 teaspoons ketchup; 1/8 teaspoon sugar; 1/8 teaspoon pepper; 2 hamburger buns; 8 oz 80 percent ground beef; 1/4 teaspoon vegetable oil; 1/4 teaspoon kosher salt, divided; 2 slices American cheese; 2 romaine lettuce leaves; 1 roma tomato