Chop the cabbage into coarse shreds and dice the carrots and onion. Prepare all ingredients before starting for a smooth process.
In a skillet over medium heat, sauté the diced onion and carrots with a splash of oil until they become fragrant and translucent, about 5 minutes. This deepens their sweetness and flavor.
Transfer the sautéed vegetables to the slow cooker, then add the shredded cabbage and tomato paste. Pour in the broth and stir well to combine everything evenly.
Stir in smoked paprika, chili flakes if using, and season generously with salt and pepper. Mix thoroughly so all vegetables are coated with the smoky spice.
Set your slow cooker to low and cook for 6 to 8 hours, until the cabbage is silky and the broth is deeply flavored. The aroma will fill your kitchen with smoky richness.
Once cooked, taste the broth and adjust seasoning with more salt, pepper, or a squeeze of lemon if you like a brighter flavor. Give it a gentle stir to redistribute the flavors.
Serve hot, garnished with fresh herbs if desired, and enjoy this cozy, deeply flavored cabbage soup that tastes like it simmered all day.