In a medium bowl, combine the flour, sugar and salt. Stir to combine and whisk in the eggs until the mixture is smooth.
In a large, heavy-bottomed saucepan, heat the milk until scalded. Remove the milk from heat and slowly whisk 2 cups of the hot milk into the flour and egg mixture. Return this tempered flour mixture to the saucepan with the scalded milk and cook, whisking constantly, over low heat until the mixture starts to thicken and boils, about 10 minutes.
Immediately remove from heat and strain the pastry cream into a bowl, scraping out the pan with the spatula. Stir the vanilla into the strained pastry cream. Stir with the spatula to facilitate the cooling, and cover with parchment or waxed paper. Refrigerate until very cold.
Meanwhile, in the bowl of a food processor, combine the flour, sugar and baking powder. Add the butter and pulse until the mixture resembles coarse crumbs. Add the eggs and pulse again until dough comes together in pieces. Turn the dough out, make into a ball and divide into 2 portions, one that's 1/3 of the total, and the other that's 2/3 of the total. Flatten each portion into a disk, wrap each in waxed paper or parchment and chill for at least 1 hour.
Preheat the oven to 350 degrees.
Roll the larger disk into a 16-inch circle and fit it into a buttered 10-inch tart pan with 11/2-inch sides. Allow the dough to slightly overlap on the edges.
Roll the remaining disk into a 10-inch circle and cut into 10 1-inch strips. Lay the strips across the pastry cream in a lattice pattern. Brush the lattice with the remaining egg wash and bake on a cookie sheet in the lower third of the oven for 35 minutes, turning after 20 minutes.
Let cool 30 minutes before removing from tart pan and serving.