Add chopped onion to an oiled skillet and cook for 5-6 minutes until softened and translucent. Stir in the dried thyme and minced garlic and cook for an additional minute; then remove from heat.
In a large bowl, combine ground pork, cooked rice, 1 teaspoon of paprika, salt, pepper, eggs, and the cooled onion-garlic mixture. Mix gently with your hands until the ingredients are well blended.
Spread 1 cup of the sauerkraut at the bottom of a large Dutch oven. Take each blanched cabbage leaf and place about 1/3 cup of the meat mixture in a log shape at the base, then tuck and roll tightly.