Preheat the oven to 400 degrees.
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 degrees. 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 nonstick pan on medium heat. Add the leeks and saute 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. Let stand 5 to 10 minutes before cutting into wedges and serving warm.