Preheat the oven to 400 degrees. Cut the potatoes in half or quarters into a bowl. Add 2 tablespoons of the olive oil, 3/4 teaspoon of salt and the pepper. Mix and put on a baking sheet in a single layer. Bake the potatoes for 40 minutes flipping twice during baking. Make sure they turn a nice golden brown. Take out of the oven and allow to cool.
In a bowl combine 1/2 teaspoon of salt, 1 tablespoon of olive oil, the chopped garlic, mayonnaise, lemon juice and Dijon mustard. Mix and pour over the cooled potatoes.