Heat the oven to 425°F. Squeeze the potatoes in a clean kitchen towel, then mix with 2 tablespoons oil and 1/2 teaspoon salt.
Oil a metal 9-by-13-inch pan with 1 teaspoon of the remaining oil. Press the potatoes firmly across the base and slightly up the sides; bake for 25 minutes until the edges begin browning.
Cook the drained leeks in the remaining 2 teaspoons oil over medium heat for 8 minutes, until soft and their moisture has evaporated. Stir in the diced cooked sausage.
Reduce the oven to 350°F. Spread the leek mixture and fontina over the crust. Whisk the eggs, milk, remaining salt and pepper and pour them on top.
Bake for 30 to 35 minutes, until the center reaches 165°F and has no liquid pocket. Rest for 10 minutes before cutting through the potato crust.