Heat olive oil in a large pot over medium heat.
Add the chopped onion, carrots, celery, leeks, and garlic.
Cook for 10 minutes until they soften.
Pour in the canned tomatoes and vegetable stock.
Stir well to combine all ingredients.
Add borlotti beans, kale, and rosemary sprigs into the pot.
Bring everything to a boil.
Reduce the heat to low and cover the pot with a lid.
Let it simmer for about 25 minutes.
Taste and season with salt and pepper as needed.
Remove rosemary sprigs before serving.