Step 1 - Boil the Potatoes Correctly
Add the peeled, cubed potatoes to your stock pot. Cover completely with water and add a generous pinch of salt to the water this seasons the potatoes from the inside as they cook, which matters significantly more than seasoning after the fact. Bring to a boil over high heat.
Once boiling, reduce the heat to medium and cook for about 5 minutes, or until the potatoes are just barely fork-tender. This timing is the single most important detail in this entire recipe. Do not overcook them. Overcooked potatoes break down into the beginning stages of mashed potatoes, and once that happens, there's no rescuing the texture. Test frequently after the 4-minute mark a fork should slide in with slight resistance, not glide through effortlessly.
Step 2 - Drain and Cool
Drain the potatoes thoroughly in your colander and transfer them to the large mixing bowl. Let them cool for about 5–10 minutes before adding any other ingredients. This cooling step matters adding mayo-based dressing to hot potatoes causes the dressing to break down and separate slightly, and it also continues softening the potatoes past the point you want. A brief cool-down preserves the texture and keeps the dressing properly emulsified.
Step 3 - Combine Everything
Add the celery, minced white onion, sweet pickle relish, vegan mayo, yellow mustard, salt, and pepper directly to the bowl with the cooled potatoes. Using a large spoon, mix everything together until well combined. Be careful not to mash or crush the potatoes during this step you're folding and combining, not stirring aggressively. A gentle hand here preserves the distinct potato cube texture that makes a good potato salad satisfying to eat.
Step 4 - Chill and Serve
Cover the bowl and refrigerate until completely cold at least 1–2 hours, though overnight is genuinely better. The chilling time is when the flavors actually develop and meld together. A potato salad eaten immediately after mixing tastes fine; the same potato salad eaten the next day after a full chill tastes significantly more cohesive and developed. Serve cold.