Preheat oven to 400°F. Line a rimmed baking sheet (a quarter sheet pan works great) with parchment paper.
In a skillet over medium heat, add 1 tbsp oil. Add the diced onion and sauté for 5–8 minutes, stirring occasionally, until softened and lightly golden. Remove from heat and set aside.
Place the ground beef onto the prepared baking sheet and press it into an even rectangle, about the size of your Hawaiian rolls. Season generously with salt and pepper.
Bake for 15–18 minutes, or until the beef is cooked through (internal temp 160°F). Carefully drain any excess grease.
Sprinkle the sautéed onions evenly over the top of the cooked beef. Add the American cheese slices on top and return to the oven for 1–2 minutes, or until the cheese is melted.
While the cheese melts, make the burger sauce. In a small bowl, mix together the mayo, ketchup, and relish.
Slice the Hawaiian rolls in half horizontally. Spread the burger sauce over the inside of the top buns.
Carefully transfer the cheesy beef patty onto the bottom buns. Place the top buns on, slice into sliders, and serve warm.