Clean the leek well: Slice in half lengthwise and rinse between layers under cold water. Thinly slice the white and light green parts.
Sauté aromatics: In a heavy-bottomed pot, heat olive oil and goat butter over medium heat. Add leeks, shallot, and celery. Sauté 5–7 minutes until soft but not browned.
Simmer: Add diced potatoes, thyme, bay leaf, salt, and pepper. Stir for 1 minute. Pour in the broth and bring to a simmer. Cover and cook for 20–25 minutes until potatoes are very soft.
Remove herbs: Fish out bay leaf and thyme sprigs.
Blend until silky: Use an immersion blender for a rustic texture, or blend in batches in a high-speed blender for a smooth, creamy finish. Return to pot.
Add cashew milk: Stir in the cashew milk and gently heat (do not boil). Adjust seasoning.
Finish with acid: Add vinegar or lemon juice to brighten the flavors.
