In a large pot, heat the olive oil over medium heat. Once hot, add the diced onions and sauté, stirring occasionally, until they are translucent and fragrant, about 5 minutes.
Add the minced garlic to the pot and sauté for an additional minute, allowing the garlic to become aromatic without browning.
Stir in the chopped carrots and diced potatoes. Continue to sauté for an extra 5 minutes, stirring occasionally to ensure the vegetables do not stick to the bottom of the pot.
Incorporate the finely chopped cabbage into the pot and mix thoroughly. Cook for approximately 3-4 minutes, or until the cabbage begins to wilt and soften.
Slowly pour in the vegetable broth and increase the heat to bring the mixture to a gentle boil.
Once it reaches a boil, reduce the heat to low, cover the pot, and let it simmer for about 25-30 minutes, or until the vegetables are tender and fully cooked.
After the simmering time, add the lemon juice, lemon zest, and chopped dill to the soup, stirring well to combine. Season with salt and pepper according to your taste.
Allow the soup to simmer for an additional 5 minutes, letting the flavors meld together, then remove from heat.
Notes
Serve hot with a dollop of crème fraîche or yogurt for added creaminess.