Keep everything cold. Keep the beef refrigerated until mixing and use a chilled bowl. Prepare a covered container and a tray that can hold the patties without overlap.
Season the beef. Put the cold ground beef in the bowl and distribute the salt, sweet paprika, and black pepper evenly over it. Leave the onion out for now.
Mix thoroughly. Work the meat by hand for 5–6 minutes, repeatedly folding, pressing, and bringing it together. This method develops a cohesive beef mixture rather than a loosely handled hamburger texture.
Add the sparkling water. Work in the very cold sparkling water gradually. Continue only until the liquid is absorbed and the mixture is evenly tacky and cohesive. Do not add extra water to compensate for very lean beef.
Chill the mixture. Press the mixture into a shallow covered container and refrigerate for 90 minutes at 40°F (4°C) or below.
Add the fine onion. Shortly before shaping, peel and very finely chop the onion. Work it evenly into the chilled mixture without unnecessarily warming the meat. Large onion pieces can make thin patties fragile.
Portion and flatten. Divide into the displayed number of equal servings. Use some of the measured oil to lightly grease shaping parchment. Flatten each portion between sheets to about 6 1/4–7 inches (16–18 cm) across and 3/8 inch (1 cm) thick, making the center slightly thinner than the rim.
Chill the patties. Lay the shaped patties side by side on a suitable tray, cover, and refrigerate for another 30 minutes. Keep any portions waiting for later cooking batches refrigerated.
Preheat the cooking surface. Fully preheat a grill, griddle, or large suitable skillet. Lightly brush the cooking surface with the remaining measured oil as appropriate for the equipment; follow its heat-use instructions. Remove all shaping parchment before cooking and keep it away from flame.
Cook and turn carefully. Transfer the cold patties to the hot surface with space between them. Cook about 5–6 minutes per side, turning with a wide spatula once the first side has formed a crust and releases readily. Do not press on the patties; adjust heat if the outside darkens too fast.
Check the center. Insert a clean tip-sensitive thermometer sideways into the center of the thickest area of each thin patty. It must reach at least 160°F (71.1°C) before removal. Continue cooking if needed; do not judge safety by surface browning, interior color, or a fixed time alone.
Serve on clean plates. Transfer to a clean plate and serve promptly. Offer warm bread, extra raw onion, ajvar, grilled peppers, or salad separately if desired. Never return cooked meat to the unwashed raw-meat tray.
Store leftovers promptly. Refrigerate cooked leftovers in shallow containers within 2 hours, or within 1 hour above 90°F (32°C). Keep at 40°F (4°C) or below, use within 3–4 days, and reheat throughout to 165°F (74°C).