Heat 2 tablespoons of olive oil and 2 tablespoons of butter in a large pot over medium heat. Add the onion, celery, carrot, and leek, and cook for 7-8 minutes, stirring occasionally, until the vegetables are softened and fragrant.
Add the garlic and celery leaves and cook for about 30 seconds, just until fragrant. Pour in the white wine to deglaze the pot, scraping up any bits from the bottom. Let it simmer for 2-3 minutes, until mostly reduced.
In a separate container, whisk together 4 teaspoons of Knorr Roasted Vegetable Base with 4 cups of hot water to make the broth. Once dissolved, pour it into the pot along with the potatoes, bay leaf, Parmesan rind, and 2 more cups of hot water. Stir and bring to a gentle simmer. Cook for about 10 minutes, until the potatoes start to soften.
Add the ditalini and pinto beans, stirring occasionally as the soup simmers for about 8 minutes, until the pasta is tender. Add a bit more hot water or broth as needed to reach your preferred consistency. Remove the bay leaf and Parmesan rind.
While the soup is simmering, make the pesto. In a small blender or food processor, blend the basil, walnuts, garlic, Parmesan, lemon juice, salt, and olive oil until smooth, adjusting with more lemon juice or oil if needed.
Stir a few spoonfuls of pesto into the soup off the heat. Season with salt and pepper if needed.
Ladle into bowls and finish with a drizzle of olive oil, some freshly-cracked black pepper, extra celery leaves, and an extra dollop of pesto.