In a bowl, gently combine ground beef, grated onion, egg, breadcrumbs, salt, and pepper. Mix just until incorporated; do not overwork the meat.

Divide the meat mixture into 6 equal portions and form them into thin patties, slightly wider than your hamburger buns.

Chill the patties in the refrigerator for at least 30 minutes to help them hold their shape during cooking.

While the patties chill, prepare the sauce. Heat olive oil in a saucepan over medium heat. Add minced garlic and sauté for about 30 seconds until fragrant, being careful not to burn it.

Stir in the crushed tomatoes, ketchup, water, sugar, and a pinch of salt and pepper. Bring the sauce to a simmer, then reduce heat and let it cook gently for 10-15 minutes, allowing flavors to meld.

In a separate skillet, cook the chilled patties over medium-high heat for about 3-4 minutes per side, until browned but still slightly pink in the center.

Lightly toast the inside of the hamburger buns. Dip the cut sides of the buns into the warm sauce.

Assemble the burgers: place a cooked patty onto the bottom half of a sauce-dipped bun. Spoon additional sauce over the patty.

Place the top half of the sauce-dipped bun over the patty. Loosely cover the assembled burgers with a lid or foil and steam over low heat for about 5-7 minutes, until the buns are soft and infused with the sauce.

Serve immediately while hot and enjoy the uniquely tender and flavorful experience.