Set a large skillet over low heat and add 2 tablespoons of the butter. When the butter is melted, add the thinly sliced onion. Saute the onions for 35 minutes, stirring occasionally, until golden brown and caramelized.

In a large bowl, combine the vegan ground beef with 1 1/2 teaspoons beef-style base, 3/4 teaspoon Worcestershire sauce, and ground black pepper. Transfer to the skillet with the onions and cook over medium heat, using a spatula to break up any large clumps, for 5 minutes or until browned. If needed, drain off any excess grease.

Preheat the oven to 350°F and line a baking sheet with aluminum foil. Separate the buns into individual pieces and arrange the bottom buns on the prepared baking sheet so they are touching.

Distribute the beef/onion mixture over the bottom buns in an even layer. Sprinkle with cheese and cover with the top buns.

In a small microwave-safe bowl, use the microwave to melt the remaining 3 tablespoons of butter. Stir in the remaining 1 1/2 teaspoons beef-style base, and 1 1/2 teaspoons of Worcestershire sauce until combined. Use a pastry brush to brush the beefy butter mixture over the top of the buns.

Wipe out the small bowl then combine the sesame seeds, thyme leaves, garlic powder, and onion powder. Sprinkle over the top buns.

Bake for 20 minutes, until the cheese is melted and the tops of the rolls are golden brown. Serve hot.