In a large bowl, whisk the eggs and then mix in the breadcrumbs. Let it sit for about 2 to 3 minutes until soaked.
Mix in the ground beef, minced onions, garlic cloves, Worcestershire sauce, Tabasco sauce, salt, and pepper until combined.
Form 6 equal-sized hamburger steak patties and place them on a plate.
Heat olive oil in a large rondeau or sauce pot over medium-high heat for about 90 seconds.
Cook the hamburger steaks for 3 to 4 minutes on each side until browned.
Remove the patties and add the sliced onions to the pot, seasoning them with salt.
Sauté the onions for about 5 minutes, then reduce heat to low and cook for another 10 to 12 minutes until caramelized.
Stir in the garlic and cook for 30 to 45 seconds until fragrant. Then sprinkle in the flour and mix.
Pour in the beef stock and bring to a boil, seasoning gently with salt and pepper.
Add back the hamburger steaks, cooking for another 5 to 6 minutes to heat through. Stir in butter and serve.