Put vegan butter, zucchini, celery, fennel, asafoetida, pink salt, pistachios, and 1 cup water in a large pot.
Cover with lid, and cook on medium heat for about 20 minutes, or until all the vegetables are mushy and the pistachios are soft. Remove from heat and allow to cool slightly.
Put soup ingredients and mint leaves in a blender and combine at high speed until super smooth, adding up to 1⁄2 cup water for consistency.
Pour into a bowl, drizzle with olive oil oil, sprinkle with sesame seeds, and serve.