Heat the butter in a large pot on medium high heat. Once melted, add in the carrot, onion, celery, and parsley and cook, stirring frequently, for 5 minutes.: As the vegan butter melts you should hear a gentle sizzle and smell a light, toasty aroma, indicating the fat is hot enough to soften vegetables. Keep the heat steady so the butter does not brown too quickly, that would push the flavor toward bitterness. If your butter smokes, lower the heat immediately to avoid burnt notes, which are hard to mask later.
Add in the flour and cook, stirring constantly, for 2 minutes.: You will notice the onion turn translucent and the edges of the carrot and celery soften, releasing a sweet vegetal scent. Frequent stirring ensures even softening and prevents sticking. If you skip stirring, pieces at the bottom may brown unevenly, creating pockets of bitter flavor, so keep the motion regular.
Stir in the broth. Add in the potato, milk, and salt. Boil for 2 minutes. Reduce the heat, cover and simmer gently for 25 minutes.: When you add the flour , it will coat the softened vegetables and start to toast, smelling slightly nutty as it cooks. Stirring constantly prevents lumps and removes the raw flour taste, which is crucial because raw starch can leave a chalky finish. If you see clumps forming, lower the heat and stir vigorously until the mixture smooths out.
Finally, remove the lid and bring to a boil for 2 more minutes, just until it starts to thicken.: As you pour in the vegetable broth you will hear a soft bubbling and the kitchen will begin to smell savory and inviting. Once the potato and cashew milk join, bring the liquid to a brief boil to activate the thickening from the flour , then reduce to a gentle simmer so the cubes cook through without breaking apart. The simmer should be a low, steady bubble; vigorous boiling can shred the potato and make the texture gluey. Watch early in the simmer to ensure a gentle heat and adjust as needed.
Transfer 1 cup to a high-powered blender and purée. Stir back into the soup.: Removing the lid concentrates flavors and lets the soup thicken as water evaporates slightly; you will see tiny bubbles and a sheen forming. This is the moment the soup develops body from the cooked flour and released potato starch. If you overboil, the soup may reduce too far and become overly dense, so watch closely and stop once the broth looks pleasantly thicker and coats a spoon.
DEVOUR!: When you blend a portion, you create silkiness while preserving chunk for texture contrast, and the whirring sound will change from bubbling to a steady motor hum. Use caution with hot liquid in a blender by venting the lid slightly so steam can escape, preventing pressure buildup. If you don’t vent, hot soup can force the lid off, making a dangerous mess.
Stir back into the soup: After returning the puréed portion, the pot will become luxuriously creamy, with small potato pieces distributed throughout. Stir to combine until the color and texture are uniform, and taste to adjust seasoning. A common mistake is to over stir vigorously, which can break remaining potato pieces into too small fragments; stir gently until homogenous.
DEVOUR!: The final sensory reward is the warm bowl in your hands, steam rising, and the first spoonful that is creamy, slightly thick, and well seasoned. Take a moment to taste and note if a pinch more salt is needed to lift the flavors. A rushed bite may miss nuances, so let it cool slightly and savor the layered aroma before eating.