In a large bowl, combine onion, garlic, thyme and one cup cheese. Crumble beef over top and mix well. Form into 6 oval-shaped patties. In a large skillet, cook patties over medium heat for 5 to 6 minutes per side, to desired doneness.
Meanwhile, prepare toast according to package directions. Drain patties; set aside and keep warm.
Add remaining ingredients to the skillet. Bring to a boil; cook and stir for 2 minutes, or until slightly thickened. Return burgers to skillet; turn to coat. Sprinkle with remaining cheese. Serve burgers on toast.