Preheat oven to 350ºF. Prick the pie crust several times with a fork and prebake the pie crust for 12-15 minutes. Let the crust cool before filling.
Heat the olive oil in a skillet over medium-high heat. Saute the leeks for 5-6 minutes. Add the tarragon, water and a pinch of salt and pepper and simmer another 5 minutes until the leeks are tender. Remove from heat.
Beat together the eggs and half and half. Stir this mixture and the shredded cheese into the leeks and add salt and pepper to taste. Pour the mixture into the prebaked pie shell. Bake the pie for 40-50 minutes. Let the pie sit for 15 minutes before slicing.