Place flour, powdered sugar, and salt in the bowl of a food processor. Pulse to combine. Add the cold cubed butter and pulse (about 10–12 times) until the mixture resembles coarse sand with some butter pieces about the size of a pea.
Add the egg. Pulse until the dough begins to clump together in large moist crumbs. Squeeze a handful of crumbs; if they hold together, it’s ready. If it’s too dry and won't hold, add 1-2 teaspoons of cold water.
Turn the dough onto a work surface, gently press into a flat disc, wrap in plastic, and refrigerate for at least 2 hours (or up to 2 days).
On a lightly floured surface, roll the dough to 1/8-inch thickness.
Cut circles 1 inch wider than your tartlet tins (4.5-inch circles for a 3.5-inch tartlet tin). Gently press the dough into the corners of the tins. Trim the excess dough so it is flush with the rim. Re-roll the dough and repeat. Tip: Instead of balling up your scraps into a lump, stack the scrap pieces on top of each other and press them down flat. Cover and refrigerate for 20 minutes before re-rolling. This helps prevent shrinkage.
Prick the bottom of the dough all over with a fork. Place the shells in the freezer for 30-60 minutes.
Preheat oven to 350°F.
Bake the chilled shells for 12–15 minutes or until very lightly golden just around the edges. If the middle has puffed up, use a spoon to gently press it down after baking. Let them cool completely in the tins before removing.