Prepare the cabbage leaves: Gently rinse the sour cabbage leaves under cold water if they are especially salty. Carefully separate the leaves and keep them whole. Use a small knife to trim the thick stem at the base of each leaf without cutting through the leaf. Reserve the smaller or torn leaves for lining the pot.
Prepare the vegetables: Finely chop the onion and garlic, then grate the carrot. Alternatively, pulse the vegetables briefly in a food processor until finely chopped. Avoid blending them into a watery puree.
Rinse the rice: Place the uncooked rice in a fine-mesh strainer and rinse it under cold water until the water runs mostly clear. Drain thoroughly before adding it to the filling.
Prepare the filling: Combine the ground meat, rice, onion, carrot, garlic, smoked meat, sweet paprika, salt, black pepper, and optional mixed seasoning in a large bowl. Mix until everything is evenly distributed and the filling holds together. Avoid overmixing.
Fill the cabbage leaves: Place one cabbage leaf on a clean work surface with the trimmed stem end closest to you. Add a spoonful of filling near the base and shape it into a small log. Do not overfill because the rice will expand during cooking.
Roll the sarma: Fold both sides of the cabbage leaf inward over the filling. Roll the leaf forward from the base toward the tip, creating a compact roll. Repeat with the remaining leaves and filling.
Line the pot: Cover the bottom of a large pot with the reserved small or torn cabbage leaves. This prevents the stuffed cabbage rolls from sticking or burning during cooking.
Arrange the rolls: Place the sarma closely together in the pot with the seam side facing down. Arrange them in a compact layer and add a second layer if necessary.
Prepare the cornstarch slurry: Measure the water into a large bowl or jug. Remove a few tablespoons of the cold water and mix it with the cornstarch in a small bowl until completely smooth.
Prepare the cooking liquid: Add the cornstarch slurry to the remaining water. Stir in the sweet paprika, black pepper, salt, and optional mixed seasoning.
Add the cooking liquid: Carefully pour the seasoned liquid over the stuffed cabbage rolls. They should be mostly covered. Add a little more water if necessary.
Cook the stuffed cabbage rolls: Place the covered pot over medium heat and bring the liquid to a gentle simmer. Reduce the heat to low and cook for approximately 2 hours, or until the cabbage is tender, the rice is fully cooked, and the meat filling is cooked through.
Check during cooking: Check the liquid occasionally and add a small amount of hot water if too much has evaporated. Do not stir the cabbage rolls. Gently shake the pot if necessary to prevent sticking.
Rest and serve: Remove the pot from the heat and let the sarma rest for 10-15 minutes before serving. Serve warm with sour cream, mashed potatoes, or crusty bread.