Whisk together first 3 ingredients in a large Dutch oven. Whisk in eggs, milks, and half-and-half. Add 2 tablespoons butter; place over medium heat. Cook, whisking rapidly and constantly, 18 minutes or until mixture thickens and coats the back of a spoon. (Do not boil.) Remove from heat; stir in 2 teaspoons vanilla. Set aside to cool.
Meanwhile, beat 1 cup butter and 3/4 cup sugar at medium speed with an electric mixer until creamy. Reduce speed to low, and beat in 1 cup flour and next 4 ingredients. By hand, stir in remaining 1 cup flour until mixture forms a ball. Divide dough in half. Place half of dough between 2 sheets of floured wax paper. Roll dough into an 11-inch circle. Carefully peel off top piece of wax paper, and invert dough into a 9-inch deep-dish pieplate coated with cooking spray. Repeat rolling procedure with remaining half of dough. Carefully remove top piece of wax paper, and cut dough into 1/2-inch-wide strips.
Set Dutch oven containing custard in a large bowl of ice water. Stir for about 3 minutes or until mixture is completely cooled. Pour 4 1/3 cups custard into bottom crust, reserving and chilling remaining custard for other uses. Immediately, arrange dough strips in a lattice pattern on top of pie. Seal strips to bottom crust. Bake at 350° for 45 minutes. Cool completely. Store in refrigerator.
Note: You'll have half of the custard leftover. When chilled, it makes a delicious soft custard or a sauce to serve over fresh fruit. You can spike it with rum or bourbon or make a second recipe of the crust and bake 2 tarts. For best results, if you decide to make a second tart, do not double the crust in one bowl, but prepare it as 2 separate recipes.