Place the pie crust on a baking sheet, cover the bottom of the pie crust with a coffee filter or cut a round piece of parchment paper and pour the dried rice inside the pie crust. Bake for 6 minutes.
Reduce the oven heat to 375°F. Remove and discard the rice and parchment paper or coffee filter and set the pie crust aside.
In the meantime, melt the butter in a non-stick pan over medium heat. Add the leeks and sauté for 3 minutes or until tender. Cool slightly.
Combine the eggs, cream, salt, pepper in a bowl. Pour the mixture into the pie crust.
Sprinkle the ham, leeks, and cheeses inside of the pie crust.
Bake the until a toothpick inserted into the center comes out clean (about 25 minutes). Remove from the heat, and let stand for 5 to 10 minutes before cutting into wedges and serving warm.