First, melt 2 tablespoons of butter in your skillet over medium heat, then add the sliced sweet onions. Reduce the heat to medium-low and cook the onions slowly, stirring occasionally, for about 25–30 minutes until they turn golden and slightly sweet. This low-and-slow approach is key for deep, rich caramelization.
While the onions are cooking, combine the ground beef in a bowl with half of the beef base and half of the Worcestershire sauce. Season with kosher salt and black pepper. Then add this meat mixture to the skillet with the onions, turn the heat up to medium-high, and break the beef up as you brown it, making sure it mixes well with the onions. When fully cooked, drain off any excess grease.
Preheat your oven to 350°F (175°C). Lightly grease your baking sheet. Separate the tops and bottoms of the buns, and pack the bottom halves snugly on your sheet. Spread the beef-and-onion mixture evenly over the bottoms, then sprinkle the shredded Gruyère (or Swiss) cheese on top. Close each slider by placing the bun tops back on.
In a microwave-safe bowl (or over low heat), melt the remaining 6 tablespoons of butter with the rest of the beef base and the remaining 1/2 tablespoon of Worcestershire sauce. Use your pastry brush to paint this flavorful glaze over the top buns. Then sprinkle sesame seeds, fresh thyme, onion powder, and garlic powder evenly over the glazed tops. Bake for about 20 minutes, until the cheese has melted and the tops are lightly browned.