Warm the olive oil in a large pot over medium heat. Add the onion and cook for 5 to 7 minutes until translucent.
Stir in the garlic, tarragon, salt, and pepper. Cook for 1 more minute until fragrant.
Add the asparagus and potato to the pot, followed by the vegetable broth. For a thicker soup, use 3 cups instead of 4. Bring to a boil, then reduce heat to maintain a simmer. Cover and cook for about 15 minutes until the veggies are fork-tender.
Turn off the heat. Use a handheld blender to carefully blend the soup right in the pot. See notes for upright blender instructions.
Stir the Greek yogurt into the pot.
Cover the pot, or transfer the soup to a bowl and cover, then store in the refrigerator for 2 to 3 hours until chilled.
Serve cold, topped with desired garnishes (see notes for ideas), and enjoy!
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Notes
Upright blender instructions: Transfer soup in batches. Leave the lid slightly cracked or remove the plastic circle from the center and cover with a dish towel when blending to allow steam to escape. Transfer blended soup to a large bowl and repeat until the whole soup is blended.
Possible toppings: more tarragon, goat cheese crumbles, chopped bacon, chopped walnuts
Storage: Keep in an airtight container in the fridge for up to 5 to 7 days. You can freeze for up to 3 months. Let the soup cool completely before transferring to freezer-safe containers, and leave a little headspace to allow for expansion. Thaw in the fridge before serving.