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.