Melt 1/4 cup butter in heavy large skillet over medium heat. Add sliced leaks and stir to coat. Reduce heat to medium low.
Cover and cook until leeks are tender, stirring occasionally, about 8 minutes. Uncover and cook until almost all liquid is absorbed, about 3 minutes.
rub 9x13 inch baking dish with 1 Tablespoon butter.
Mix cream and garlic in small bowl.
Arrange half of potatoes in prepared dish. Season generously with salt and pepper. Cover with leeks. Sprinkle with half of cheese. Ladle half of cream mixture over potatoes and leeks. Repeat layering with remaining potatoes, cheese (you may use either white cheddar or Gruyere cheese). and cream mixture. Sprinkle with Parmesan.
This can be prepared 6 hours ahead. Cover and refrigerate.
Let stand 1 hour at room temperature before baking. Bake until potatoes are tender and top is deep golden brown, about 1 hours and 15 minutes. Let stand 15 minutes at room temperature before serving.