Begin by preparing your ingredients: chop the cabbage into roughly 1-inch pieces, peel and dice the onion, slice the carrots thickly, and mince the garlic. Have everything ready to layer into the slow cooker.
Layer the diced onions and minced garlic at the bottom of the slow cooker to start building flavor.
Add the sliced carrots on top of the aromatics, followed by the chopped cabbage, creating a colorful, layered look.
Pour the vegetable broth over the layered vegetables, ensuring it just covers the ingredients.
Stir in the canned diced tomatoes with their juice, then sprinkle salt and pepper over the top. Add smoked paprika if you want a smoky flavor.
Cover the slow cooker and set it to cook on low for 6 to 8 hours. As it simmers, the house will fill with a fragrant, smoky aroma, and the vegetables will soften beautifully.
After cooking, open the lid and check that the cabbage and carrots are tender, and the broth is flavorful. Taste and adjust seasoning with more salt or pepper if needed.
Give everything a gentle stir to combine flavors, then serve hot in bowls, garnished with fresh herbs if desired.