Preheat the oven to 425 degrees. Lightly coat a 9-inch pie dish with non-stick spray. Mix the shredded potatoes with 2 tablespoons of oil. Spread the potatoes evenly in the pie plate. Bake in the preheated oven until the potatoes begin to brown (about 15 minutes). Remove from the oven and set aside. Meanwhile heat the remaining 1 tablespoon of oil in a skillet. Sauté the broccoli and leeks until leeks are tender (about 5-10 minutes). While the vegetables are cooking, whisk together the milk, cottage cheese, and eggs. Reduce the oven temperature to 400 degrees. Layer the sautéed vegetables on top of the browned potatoes. Sprinkle with the Swiss cheese. Pour the egg mixture on top of the cheese. Bake the quiche for 30 minutes or until the egg is set.