Preheat oven to 350. Spray a 9x13 pan with vegetable oil.

In a large skillet over medium heat, add butter, leeks, salt and pepper. Sauté for 5 minutes and add garlic and thyme. Continue cooking until the leeks are lightly browned, another 10 minutes. Set aside. (Can be made the day before and stored in the refrigerator.)

In a food processor (or slice by hand), with the 1/8-inch slicing blade, slice the potatoes and add them to a large stock pot and add half and half until it generously covers the potatoes, adding more half and half if needed. Cook over medium heat until the half and half comes to a boil. Add the cooked leeks and salt and pepper to taste and reduce heat. Gently cook the potatoes until they are most of the way cooked through, about 15 minutes. Add 2 cups of cheese and allow the cheese to melt and do not allow to boil. Taste for seasoning. (Can be made up to this point and refrigerated overnight.)

Transfer potatoes to the greased 9x13 pan and sprinkle with remaining cheese. Cover with foil and bake for 1 ½ hours. Remove foil and bake until well browned. The potatoes are done when they are easily pierced with the tip of knife, around 20 minutes. Remove from oven and allow to rest for 10 minutes before serving.