Make the dough by adding the sugar, butter, salt, baking powder and flour to the bowl of a food processor. Pulse until pea-sized crumbs form, about 20 pulses.
In a small bowl, whisk together the yolks, egg, and vanilla. Transfer the flour mixture to a large bowl and pour in the egg mixture. With a wooden spoon or rubber spatula, stir together until shaggy dough forms. Add the water 1 tablespoon at a time until the dough comes together, but is not too sticky (you may not need all 3 tablespoons).
Form a disc with the dough, wrap in plastic wrap, and chill in the refrigerator for at least 4 hours.
Roll the dough out to 1/8-inch thickness. Place a 9-inch tart pan on a rimmed baking sheet. Line the tart pan with the rolled dough and trim the edges to be level with the pan. Return to the refrigerator.
Meanwhile, make the filling by adding 3 cups of strawberries to a large sauce pan over medium heat. Add the sugar, vanilla, and flour. Continuously stir until the mixture comes to a boil. The strawberries will soften and juices will be released.
Once boiled, lower the heat and simmer for 10 minutes. Remove from heat and let sit for 5 minutes. Add the remaining strawberries and stir to combine. Cool to room temperature. While cooling, preheat oven to 375°F.
Remove the baking sheet and tart pan from the refrigerator and fill the chilled crust with the cooled filling, up to about 1/4-inch from the top. Bake with the baking sheet for 50 to 55 minutes until the crust is golden brown.
Let cool completely in the pan. Once cooled, remove the rim by placing the pan on top of a tall can or container. The border will just fall off. If not, gently tap the top of the border’s edge until it falls off.