Pumpkin Ice Cream Pie

INGREDIENTS

• 1 packet pumpkin ice cream starter
• 1 1/2 cups half-and-half
• 1 1/2 cups heavy cream
• 2 egg yolks
• 2 Tbs. very cold water, plus more as needed
• 2 tsp. vanilla extract
• 2 1/2 cups all-purpose flour
• 2/3 cup sugar
• 1/2 tsp. salt
• 16 Tbs. (2 sticks) cold unsalted butter, cut into 1/4-inch cubes
• 1 egg, lightly beaten with 1 tsp. water
• 1 cup heavy cream
• 1/8 tsp. freshly grated nutmeg
• 2 Tbs. sugar
• 1/2 tsp. ground cinnamon
• 1 tsp. vanilla extract