Finely shred half the onion. Thinly slice remaining onion; set aside.
Combine shredded onion, beef, and salt, mixing lightly but thoroughly. Lightly shape into four 1/2-inch-thick oval steaks. Sprinkle tops with additional salt and pepper, as desired.
Heat a large nonstick skillet over medium heat until hot. Place patties in skillet; cook 10 to 12 minutes to medium doneness (160°F) or until no longer pink in center, turning once. Remove from skillet; keep warm.
Add sliced onion, mushrooms, and 1/4 cup of the beer to same skillet; cook over medium-high heat 5 minutes or until vegetables are tender, stirring occasionally. Combine gravy mix with remaining beer, mixing until smooth; stir into mushroom mixture in skillet. Add half of the thyme; simmer 1 minute or until thickened, stirring frequently. Spoon sauce over patties; sprinkle with remaining thyme.
