Heat the oil in a large pot over medium-high heat. Once the oil is shimmering, add the leek, celery, and garlic. Season with salt and pepper. Cook until leeks are are soft, about 3 minutes. Add in the broth and bring to a simmer. Let simmer for 5 minutes and then add in the peas, beans, spinach, and carrot noodles. Let simmer for 5 minutes or until vegetables are crisp tender. Stir in the thyme and tarragon and let cook for another minute. Taste and adjust with more and salt and pepper, as needed.
Divide soup into bowls and top with cheese, if using.