Start by preparing your ingredients: peel and dice the carrots, chop the celery and onion into small, even pieces to help them soften uniformly.
Heat a tablespoon of olive oil in a skillet over medium heat. Add the diced onion, carrots, and celery, and cook until fragrant and slightly softened, about 5 minutes. This step enhances their flavor with a gentle caramelization and aroma.
Transfer the sautéed vegetables into your slow cooker. Pour in the crushed tomatoes and vegetable broth, then sprinkle in the crushed dried basil and oregano. Stir everything together to combine the flavors evenly.
Add the small pasta shells (or chopped zucchini if you prefer a variation), rinsed cannellini beans, and chopped greens like kale or spinach. Gently stir to distribute all the ingredients throughout the broth.
Cover the slow cooker and set it to low for 6 to 8 hours, or high for about 4 hours. During this time, the vegetables will become tender, and the flavors will meld into a hearty, savory broth filled with rich aromas.
Once cooking is complete, check that the vegetables and pasta are tender. Remove the bay leaf, and season with salt and pepper to taste. For added brightness, squeeze fresh lemon juice over the soup just before serving.
Finish by drizzling a little more olive oil over the top for a fruity aroma and silky texture. Ladle the hot minestrone into bowls, and serve with crusty bread for a complete, satisfying meal.