Place egg yolk, Dijon mustard, white wine vinegar, lemon juice, salt and white pepper in a medium bowl.
Whisk until smooth.
Add oil very slowly, a few drops at a time, whisking constantly.
Continue whisking in oil in a thin steady stream until mayonnaise is thick and glossy.
Cover mayo and refrigerate until ready to serve.
Peel potatoes if desired.
Cut potatoes into thick fries, about 1/2 inch wide.
Place fries in a large bowl of cold water.
Soak 30 minutes.
Drain fries well.
Pat fries very dry with clean kitchen towels.
Heat frying fat or oil to 300°F in a deep heavy pot.
Fry potatoes in batches until pale, softened and cooked through but not browned.
Transfer fries to a wire rack.
Let fries rest 20 to 30 minutes.
Increase frying fat or oil to 375°F.
Fry potatoes again in batches until golden brown and crisp.
Transfer fries to a clean wire rack or paper towel-lined tray.
Season immediately with salt.
Serve hot with homemade mayo.