Start by chopping the onion into small dice, then crush the garlic cloves to release their fragrant aroma.
Add a splash of olive oil to your slow cooker and turn it on low. Once hot, sauté the diced onion and crushed garlic for about 5 minutes until they become fragrant and slightly translucent.
Layer in the chopped carrots and add the diced tomatoes, distributing them evenly over the softened onion mixture.
Place the large chunks of cabbage on top of the other ingredients, then pour in the vegetable broth to cover everything.
Toss in the bay leaf and grind some fresh black pepper over the top. Cover the slow cooker with its lid and set it to low.
Let the soup cook gently for 6 to 8 hours, until the vegetables are tender and the broth has darkened in flavor, filling your kitchen with warm aromas.
Halfway through, give the soup a gentle stir to help distribute the flavors and prevent sticking. If needed, add a splash more broth to maintain the liquid level.
Once the cooking time is complete, remove the bay leaf and give the soup a final stir. Taste and adjust the seasoning with more pepper if desired.
Serve hot in bowls, enjoying the silky, hearty texture and the vibrant aroma of this comforting, slow-cooked cabbage soup.