Sauté Aromatics: In a large pot or Dutch oven, heat a tablespoon of oil over medium heat. Add the chopped onion and sauté until softened and translucent, about 5-7 minutes. Add the minced garlic and grated carrot (if using), and cook for another 3-5 minutes until fragrant.

Add Tomato Paste & Meats: Stir in the tomato paste and cook for 1-2 minutes, stirring constantly, to deepen its flavor. Add all the diced and sliced meats (ham, smoked sausage, cooked beef/chicken) to the pot. Sauté for 5-7 minutes, allowing the meats to brown slightly and release their flavors.

Combine with Pickles & Broth: Stir in the diced dill pickles, black olives, green olives, and capers (if using). Pour in the beef or chicken broth and the pickle brine. Add the bay leaves and black peppercorns.

Simmer: Bring the soup to a boil, then reduce the heat to low, cover, and let it simmer for at least 30-40 minutes. This allows the flavors to meld beautifully.

Season: After simmering, remove the bay leaves and peppercorns. Taste the soup and season with salt, pepper, and dried dill as needed. Keep in mind that the pickles and olives already add significant saltiness.

Serve: Ladle the hot Solyanka into bowls. Garnish each serving with a dollop of sour cream, a fresh lemon wedge, and a sprinkle of fresh dill. The lemon is squeezed into the soup to add a final bright, sour kick.