Slice the onion, mince the garlic, thinly slice the cabbage, and dice the potatoes into small, even 1/2-inch cubes. Thinly slice the carrot if using. Rinse and drain the beans. Set everything aside.

In a large, deep skillet or Dutch oven, heat the olive oil over medium heat. Add the sliced onion and cook for 4–5 minutes, stirring occasionally, until softened and lightly golden around the edges. Add the minced garlic and cook for 30–60 seconds, just until fragrant.

Add the sliced cabbage to the pan and sprinkle with a pinch of salt. Cook for 8–10 minutes, stirring every couple of minutes, until the cabbage softens and some edges turn lightly browned and sweet. If the pan looks dry or starts to stick, add a splash of vegetable broth or water.

Stir in the diced potatoes and sliced carrot. Toss well with the cabbage and onion mixture so the vegetables are coated in the oil and cabbage juices. Cook for 3–4 minutes, allowing the potatoes to pick up some flavor and a little color.

Add the tomato paste, smoked paprika, sweet paprika, thyme, cumin, black pepper, and soy sauce or tamari. Stir until the vegetables are evenly coated. Cook for 1–2 minutes to toast the spices and deepen the flavor.

Pour in the diced tomatoes with their juices, the white beans, and 1/2 cup vegetable broth. Stir well to combine and bring to a gentle simmer over medium heat.

Reduce the heat to medium-low, cover the skillet with a lid, and simmer for 15–20 minutes, stirring every 5 minutes. Cook until the potatoes are tender when pierced with a fork and the cabbage is very soft. If the pan looks dry, add another splash or two of broth.

Remove the lid and taste the mixture. Add more salt and pepper if needed. Stir in the fresh lemon juice. If you prefer a slightly thicker sauce, let it simmer uncovered for another 3–5 minutes.

Turn off the heat and sprinkle chopped parsley or dill over the top. Add a pinch of red pepper flakes if you like some heat. Serve hot on its own or with crusty bread, cooked grains, or a simple green salad.