Make the aioli: Combine the egg, 2 tablespoons of the oil, mustard, vinegar, garlic, and salt in a blender or the small bowl of a food processor and blend until smooth. With the motor running, drizzle in the rest of the oil in a very thin stream (this should take at least a minute) to create a thick, mayonnaise-like texture. Season with more salt to taste.

Note: If the aioli “breaks” during the emulsification process, no worries. Transfer it to a cup, then add another egg and a teaspoon of mustard to the empty blender and blend. Slowly drizzle the broken aioli back in while the motor is running to emulsify. Viola!

Make the crispy fingerling potatoes: Toss the halved fingerling potatoes in 3 tablespoons olive oil, 1 teaspoon kosher salt, and ½ teaspoon freshly ground black pepper.

Heat a heavy un-oiled baking sheet to 425°F for 10 minutes, then use oven mitts to remove the baking sheet and arrange the potatoes, cut side down, on the baking sheet and roast until the underside is crisp, 15 minutes.

Flip and roast an additional 5-10 minutes. Season with more salt and pepper.