In a large bowl, combine the Ground Beef and Ground Pork with finely grated or very finely chopped Onion. Season with Salt, freshly ground Black Pepper and a pinch of Sweet Paprika. Sprinkle in the Baking Soda, then pour in the Carbonated Mineral Water and mix gently until just combined; do not overwork. Cover and chill for at least 30 minutes to let flavors meld and the mix relax.
While the meat chills, roast the vegetables for the ajvar: place whole Red Bell Pepper and Eggplant on a baking sheet under a hot broiler or over an open flame, turning occasionally, until the skins are blackened and blistered all over (20–30 minutes). Transfer to a bowl, cover to steam for 10–15 minutes, then peel, core/seed the peppers and roughly chop both vegetables.
Make the ajvar: heat a couple of tablespoons of Sunflower Oil in a skillet over medium heat, add minced Garlic and cook briefly until fragrant. Add the chopped roasted peppers and eggplant and cook, stirring, until any excess liquid evaporates and the mixture thickens (8–12 minutes). Stir in White Wine Vinegar and Sugar, season to taste with additional salt if needed, then smash lightly with a fork or pulse briefly in a food processor for a smoother spread.
Form the chilled meat into flat patties about 1–1.5 cm thick (roughly 150–200 g each depending on size). Heat a heavy skillet or grill over medium-high heat and brush with a little oil. Cook the pljeskavice 4–6 minutes per side (longer for thicker patties), until well browned outside and cooked through to your liking.
Warm the Lepinja (Somun) Flatbread briefly on the grill or in the oven. Assemble by spreading a generous spoonful of ajvar on the bread, topping with a hot pljeskavica, and finishing with thinly sliced Red Onion for a crisp, sharp bite. Serve immediately.
