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Heat two tablespoons of the olive oil in a stockpot pot or Dutch oven over medium heat. Add the onions, carrots, and the ham. Cook, stirring every once and a while until the vegetables have softened and the onions are translucent; 8 to 10 minutes.
Add the garlic, rosemary, black pepper, and the red pepper flakes. Cook, while stirring, for one minute. Stir in the cabbage, and then pour in the canned tomatoes and their juices as well as the stock. Add the bay leaves.
Raise the heat to medium-high and bring the soup to a boil. Taste then adjust with salt. The ham does add some salt to the soup so you may not need a lot of additional seasoning.
Partially cover the pot with a lid, and then reduce the heat to maintain a low simmer. Simmer for 20 minutes or until the cabbage, and other vegetables are tender.
Remove the pot from the heat and remove the bay leaves. Stir in the lemon slices and the remaining tablespoon of olive oil. Taste and season with more salt and pepper. Serve.