Preheat oven to 350°. In a large skillet over medium-high heat, melt 2 Tbsp. butter. Add onion and thyme sprigs; season with salt and pepper. Cook, stirring occasionally, until caramelized, 30 to 40 minutes. Discard thyme.
Place bottom halves of slider buns on a large baking sheet. Top with roast beef, cheese, and onions. Close with top buns.
In a small heatproof bowl, microwave 2 Tbsp. butter until melted. Brush on top of buns. Sprinkle with parsley and garlic powder; season with salt.
Bake sliders until warmed through and cheese is melty, 10 to 15 minutes.
Meanwhile, in same skillet over medium heat, melt remaining 1 Tbsp. butter. Add garlic and cook, stirring, until fragrant, about 1 minute. Add broth, Worcestershire, and chopped thyme; season with salt and pepper. Bring to a simmer and cook, stirring occasionally, until slightly reduced, about 10 minutes.
Transfer sliders to a platter. Top with parsley. Serve with au jus alongside.
