Preheat the oven to 350°F (175°C).
Dice the 1 medium white onion into small pieces (about 1/4"–1/2").
Heat 1 teaspoon oil in a medium saucepan or skillet over medium heat. Add the diced onion and sauté until fragrant and soft, about 3 minutes.
Add 1/2 cup water and 1 teaspoon Worcestershire sauce to the pan with the onions. Bring to a boil, then reduce heat and simmer for 8 minutes. Remove from heat and set the onions and their juices aside.
Place the 1 pound lean ground beef on a sheet of parchment paper. Flatten the beef with a rolling pin or your hands into an even rectangle about 1/4" thick.
Evenly sprinkle 1/2 teaspoon salt and 1/2 teaspoon black pepper over the flattened beef.
Using a sharp knife or pizza cutter, cut the beef rectangle into 12 equal patties.
Use a metal straw or the handle of a wooden spoon to make several small vent holes in each patty (this helps them steam during baking).
On a large baking sheet, spread the cooked onions and their juices evenly to form a thin layer across the sheet. Place the 12 patties on top of the onion layer.
Cover the baking sheet with a second baking sheet turned upside down or with a large sheet of foil to trap steam. Bake in the preheated oven for 10 minutes.
Carefully remove the cover (watch for steam). Immediately place one half of an American cheese slice on each hot patty so the cheese can soften.
To assemble each slider: place a bottom slider bun, a spoonful of the cooked onions (from the baking sheet), a cheesed patty, 2 dill pickle chips, then the top bun. Serve warm.