Slice the cabbage and chop all vegetables into small, even pieces to ensure consistent cooking.
Heat olive oil in a pot and sauté the onion until soft and lightly translucent.
Add carrots, celery, and garlic, stirring briefly until fragrant.
Stir in crushed tomatoes, cumin, salt, and pepper, then add cabbage and water, cover, and cook until softened.
Add the rice and additional water, stirring to distribute evenly.
Simmer gently, stirring occasionally, until the rice is tender and has absorbed most of the liquid.
Finish with fresh dill and lemon juice, cook briefly, then adjust seasoning and serve warm.