Heat the olive oil in a large pot over medium heat. Add the onion and garlic and cook until the onion is translucent, about 3 minutes. Stir in the potatoes, carrots, zucchini, and green beans. Season with a bit of salt and cook, stirring for 3 to 4 minutes to release the vegetables' aromas. Add the tomatoes, stock, and thyme and turn the heat down to low. Season with salt (if still needed) and pepper to taste. Simmer for at least 15 minutes, and up to Before serving, stir in the white beans and heat through. Serve with a dollop of pesto and bit of grated Parmesan.