Create a beurre manié (equal parts vegan butter and flour) and whisk it into simmering broth to achieve silky creaminess without dairy, while avoiding lumps by incorporating it gradually off-heat first.

Caramelize your diced onions, celery, and carrots for 5-7 minutes in vegan butter before adding liquid to develop deep, sweet notes that elevate the entire soup's complexity.

Partially blend the cooled soup with an immersion blender—leaving some chunks intact—to create a naturally thick, creamy consistency that mimics traditional potato soup without any dairy products.

Use Russet or Yukon Gold potatoes rather than waxy varieties; they break down slightly during cooking to naturally thicken the broth while maintaining structural integrity in each spoonful.

Add salt and pepper incrementally throughout cooking, then taste and adjust aggressively at the end with extra pepper and a pinch of nutritional yeast for umami depth that compensates for missing dairy.