Preheat the oven to 350°F. In a large skillet over medium-high heat, melt 2 tablespoons of butter. Add the sliced onion and thyme sprigs, seasoning generously with salt and freshly ground black pepper. Stir occasionally, allowing the onions to slowly caramelize, deepening in color and flavor. This process takes about 30 to 40 minutes. Once caramelized, remove the thyme sprigs and discard them.

Arrange the bottom halves of the slider buns on a large baking sheet. Evenly layer the roast beef over the buns, followed by the provolone slices and the caramelized onions. Gently press the top halves of the buns over the filling.

In a small microwave-safe bowl, melt 2 tablespoons of butter. Using a pastry brush, spread the melted butter evenly across the tops of the buns. Lightly sprinkle them with parsley, garlic powder, and a pinch of salt to enhance their flavor.

Place the sliders in the oven and bake for 10 to 15 minutes, or until the cheese is melted and the sliders are warmed through.

Meanwhile, return the skillet to medium heat and melt the remaining tablespoon of butter. Add the minced garlic and sauté for about a minute, stirring frequently, until fragrant but not browned. Pour in the beef broth, Worcestershire sauce, and chopped thyme, seasoning with salt and pepper to taste. Bring the mixture to a gentle simmer, stirring occasionally. Allow it to reduce slightly, about 10 minutes, intensifying the depth of flavor in the au jus.

Once baked, transfer the sliders onto a serving platter and garnish with additional parsley for a fresh pop of color. Serve immediately with the warm au jus on the side for dipping.