This classic recipe calls for steaming the mussels in white wine, which lends acidity and creates a flavorful sauce.
1 tsp. Dijon mustard
1 egg yolk
1 cup canola oil, plus more for frying
2 tsp. white wine vinegar
2 tsp. fresh lemon juice
½ tsp. kosher salt, plus more to taste
Freshly ground black pepper, to taste
2 lb. Yukon Gold potatoes, peeled and cut into ¼"-thick sticks
2½ lb. mussels, debearded and scrubbed
⅔ cup dry white wine
2 tbsp. unsalted butter, cubed
3 ribs celery, finely chopped
1½ leeks, light green and white parts, cut into ¼"-thick slices
½ large yellow onion, finely chopped
1. Make the mayonnaise: In a large bowl, whisk mustard and egg yolk. Whisking constantly, slowly drizzle in oil in a thin stream until it begins to emulsify; whisk in vinegar, lemon juice, salt, and pepper. Set aside.
2. Make the fries: Pour oil into a 6-qt. Dutch oven to a depth of 2", and heat over medium-high heat until a deep-fry thermometer reads 375°. Add potatoes and cook until tender, about 8 minutes. Using a slotted spoon, transfer fries to a rack set over a rimmed baking sheet; chill.
3. Increase oil temperature to 385°. Working in batches, add chilled potatoes and cook until golden brown and crisp, about 4 minutes. Using a slotted spoon, return fries to rack; season with salt.
4. Meanwhile, make the mussels: Heat a 12" high-sided skillet over high heat. Add mussels, wine, butter, celery, leeks, and onions; season with salt and pepper, and cover skillet. Cook, occasionally shaking skillet, until all mussels are opened, about 5 minutes. Divide mussels between 2 large bowls. Serve with fries and mayonnaise.