Combine the flour, sugar, baking powder, and salt in the bowl of a food processor fitted with the metal blade. Pulse several times to mix.
Add the butter and pulse repeatedly until the butter is finely mixed into the dry ingredients - you do not want any visible pieces of butter.
Add the egg, egg yolk and water. Pulse repeatedly until the dough forms a ball.
Invert the food processor bowl over a floured work surface to turn out the dough. Carefully remove the blade and transfer any dough on it to the work surface. Form the dough into a disk about ½ inch thick. Wrap the dough in plastic and refrigerate it if not using immediately.
When you're ready to place dough in the tart pan: Place the dough on a floured work surface, dust it lightly with flour, and knead for about 15 seconds, squeezing and folding it over on itself so that it becomes malleable but remains cool. Shape the dough into a disk.
Start rolling the dough by rolling away from you to the far end and back again without rolling over the ends. Use a firm but gentle pressure - pressing too hard might cut right through the dough. Turn the dough 45 degrees as before and roll again. Continue turning and rolling until the dough is the desired size. As you roll, don't forget to add pinches of flour as needed. For a 1-inch deep tart pan, the dough should be rolled about 3 inches larger than the diameter of the pan.
This dough will most likely come apart in places as you place it in your tart pan. That is fine. Just pinch breaks and smooth together. This dough is very forgiving.
Continue pressing with your finger tips until evenly pressed into pan and up the sides.
Bake according to the recipe you're filling the dough with.
See my post for lemon tart in sweet tart dough for one baking option.