Place a large skillet over medium heat with the olive oil and butter. Add the onions, garlic, and thyme to the pan and cook, stirring occasionally, until the onions begin to soften, 3 to 4 minutes.
While the onions are cooking, season the Rocket Patties with salt and pepper. Push the softened onions to the outer edge of the skillet and add the burgers to the pan. Cook the burgers until browned on one side, 2 to 3 minutes, and then flip them over. Add the beer, Rocket Fuel and Dijon mustard to the pan and swirl it gently to combine all of the ingredients. Continue cooking the burgers to your desired doneness, about 4 minutes for medium. Once the burgers are finished, remove them to a plate and continue reducing the liquid in the pan until it reaches a glossy, gravy-like consistency. Season with salt and pepper.
Serve the burgers on a toasted slice of sourdough bread layered with sliced tomato. Top each burger with the onions and pan sauce and garnish with the blue cheese.