Heat a 5-quart pot over medium to medium-high heat. Once hot, add the oil and the cabbage. Cook until the cabbage starts to wilt, about 6 to 8 minutes, stirring occasionally.
Add the beef, onion, and garlic, cover the pot, and cook until the meat is browned, about 6 to 8 minutes, stirring occasionally to break up the meat.
Stir in the tomatoes (with their juices), coconut sugar, salt, thyme, black pepper, and smoked paprika. Cover the pot and cook 5 minutes, stirring occasionally.
Serve warm, garnished with parsley if desired.
Notes
Paleo and Whole30: This recipe is paleo as written. To make it Whole30 compliant, omit the coconut sugar.
Low Carb Version: Use keto brown sugar instead of coconut sugar. Without the coconut sugar, this recipe has 12g net carbs per serving.