Prepare oven and baking dish: Preheat oven to 350°F. Coat a 13- x 9-inch baking dish with cooking spray, and set aside.

Slice rolls: Using a serrated bread knife, cut rolls in half horizontally, keeping top and bottom halves intact; place bottom half of rolls in prepared baking dish, and set aside.

Cook onions: Melt 1 tablespoon of the butter in a medium nonstick skillet over medium-high. Add onions, and cook, stirring often, until softened, about 2 minutes. Reduce heat to medium, and cook, stirring occasionally, until golden brown and soft, about 15 minutes. Remove from heat, and set aside.

Assemble sliders: Arrange roast beef slices evenly over bottom half of rolls. Top evenly with cheese and caramelized onions, and place top half of rolls over cheese and onions.

Brush rolls with butter-brown sugar sauce: Melt brown sugar and 4 tablespoons of the butter in a small saucepan over low, stirring occasionally, until sugar is dissolved, about 5 minutes. Remove from heat, and whisk in mustard and salt. Brush top and sides of rolls with butter mixture, and sprinkle with 1 teaspoon of the thyme.

Bake sliders: Loosely cover baking dish with aluminum foil, and bake in preheated oven for 10 minutes. Remove foil, and bake in preheated oven until top buns are golden brown and cheese is melted, about 10 minutes.

Make au jus: Meanwhile, melt remaining 1 tablespoon butter in a small saucepan over medium. Add garlic, and cook, stirring constantly, until fragrant, about 30 seconds. Stir in beef broth, Worcestershire, and remaining 1 ½ teaspoons thyme. Bring to a simmer over medium; cook, undisturbed, until reduced slightly, about 10 minutes. Serve hot sliders with au jus.