Cook the base. Heat the oil in a large pot over medium heat. Add the onion, carrot, and celery with a pinch of salt. Cook for 6 to 8 minutes, stirring now and then, until softened.
Add the garlic. Stir in the garlic and thyme and cook for 1 minute, until fragrant.
Simmer. Add the potato, broth, tomatoes (if using), bay leaf, salt, and pepper. Bring to a boil, then lower the heat and simmer, partly covered, for 15 to 20 minutes, until the potato is fork-tender. If using peas, green beans, or spinach, stir them in for the last 2 to 3 minutes.
Blend. Remove the bay leaf. Using an immersion blender right in the pot (or working in batches in a countertop blender), blend the soup until completely smooth and creamy.
Season and serve. Taste and adjust the salt and pepper, stir in a squeeze of lemon, and serve topped with fresh parsley and crunchy croutons.