In a large pot, gently heat the olive oil. Add the onions and garlic and cook until softened, about 5 minutes. Add the tomato paste and cook 2–3 minutes more. Add the diced tomatoes and season with salt. Bring to a gentle boil, then lower the heat and simmer, partially covered, for 30–60 minutes. Meanwhile, prepare the cabbage and steam the rice.

Bring a large pot of salted water to a boil. Using a paring knife, remove the core from the cabbage and add it to the boiling water. Boil for about 10 minutes, turning halfway through, until the leaves are soft and pliable. Transfer the cabbage to a bowl and let cool slightly, then gently separate the leaves. Trim the thick center rib from each leaf by cutting a narrow V-shape at the base so the leaves roll easily without tearing.

In a bowl, combine the ground meat, rice, onion, garlic, egg, paprika, salt, and pepper.

Place 2–3 tablespoons of filling onto each cabbage leaf, fold the sides in, and roll up tightly.

Nestle the cabbage rolls into the sauce, seam-side down. Dot the top with butter and cover.

Cover and cook on the stovetop over low heat for 1½ hours, or bake at 350°F for 1–2 hours, until the cabbage is tender.