In a large pot or dutch oven over medium heat, melt vegan butter. Add chopped leeks and celery. Cook for about 10 minutes, stirring frequently.
Add salt, pepper, thyme, and garlic. Cook for 1 minute until garlic is fragrant.
Add vegetable broth, potatoes, beans, water, and bay leaf. Stir and bring to a boil. Cover, reduce heat, and simmer for 20 minutes until potatoes are fork tender.
Add soup to a blender and add almond milk. Blend until smooth (you may need to do this in batches). You can also use an immersion blender for this step.
Add soup back to the pot on low heat and stir. Taste and adjust seasonings if needed.
Garnish with fresh thyme (optional).
Once cooled to room temperature, potato and leek soup can be transferred to a sealed container and kept in the fridge for up to 4 days.To freeze the soup, put in an airtight and freezer-safe container, and wrap in a layer of aluminum foil. Then keep in the freezer for up to 3 months. Let the soup defrost in the fridge overnight before you plan to reheat.Reheat vegan leek and potato soup in the microwave in short, 30-second bursts, stirring in between, until hot. Or you can reheat in a small saucepan on the stovetop over medium-low heat.