To ensure a nice browned top to your sliders, check that the broiler flame is on when you pop them in. Many broilers cycle on and off as they work, so it's important to broil these fast-cooking burgers during an "on" cycle.
Heat the oil in a large skillet over medium heat and add the onions, spreading them into an even layer. Cook, without stirring, until the edges of the onions are beginning to brown, 5 minutes. Stir the onions and continue to cook, stirring occasionally, until browned and caramelized, another 20 minutes. Add the chipotles, garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook until fragrant and well combined, 1 to 2 minutes, and remove from the heat.
Preheat the oven broiler. Divide the meat into 12 portions, about 2 ounces each. Form a patty around each piece of cheese and flatten to 2 1/2 to 3 inches in diameter. Put the wrapped patties on a foil-lined baking sheet and sprinkle all the patties with 3/4 teaspoon salt.
Broil until the cheese is melted and the burgers are still a bit pink inside, about 6 minutes. The burgers will be cooked to at least medium in order to melt the cheese but still stay juicy.
Mix the ketchup, balsamic and 1/4 teaspoon pepper in a small bowl. Brush the burgers with some of the ketchup sauce and divide the rest among the bottom halves of the buns. Place a burger on each bottom bun, top with some of the spicy onions and finish with a top bun. Serve warm.