Preheat the oven to 375°F and generously grease a 9 x 9 x 2-inch baking dish.
Scrub the potatoes and cut them into 3/4-inch cubes. Transfer to a saucepan, add 1 teaspoon salt and cover with cold water.
Bring the potatoes to a boil and cook just until tender when pierced with a knife, 12 to 14 minutes. Do not overcook. Transfer to a colander to drain and set aside.
Heat the milk in the microwave or a separate saucepan until very warm, but not scalded. Set aside.
Melt the butter in the saucepan over medium heat. Sprinkle in the flour and blend with a whisk until well combined. Continue cooking, whisking constantly, until the mixture develops a pale golden color, about 2 minutes.
Gradually add the warmed milk, whisking continually until smooth and well blended. Continue cooking, whisking frequently, until the sauce is smooth and beginning to thicken.
Reduce the heat to low, add 1/2 cup of the shredded fontina and stir until completely melted. Add the cottage cheese, salt and pepper and continue stirring until the curds have melted and the sauce is smooth.
Return the potatoes to the pan, add the chives (reserving about a teaspoon for garnish if desired) and combine thoroughly.
Transfer the potato-cheese mixture to the prepared pan, smooth the top and sprinkle with the remaining 1/4 cup of fontina.
Bake, uncovered until golden brown and bubbly, 35 to 45 minutes. Garnish with extra chives and serve immediately.