Add the butter and sugar to the bowl of a stand mixer. Beat on a medium low speed until smooth.
Scrape the bowl down and add the egg. Mix on a low speed just until the egg starts to incorporate, but is not fully combined.
Scrape the bowl down. Add the pistachio flour and salt to the stand mixer. Beat on a medium low speed until fully incorporated. Scrape the bowl down.
Add the flour and beat on low until only just combined. A few streaks of flour okay. If needed, finish mixing the dough by hand with a spatula.
Divide the dough into two equal portions. Wrap them in cling wrap and chill in the fridge for 10- 15 minutes.
Place one portion of dough in between two sheets or parchment paper. Roll the dough out to 2mm (1/16 in), or slightly thinner. Place the dough (still between the paper) flat in the freezer. Repeat this step with the other portion of dough.
Freeze the two dough sheets for 20- 30 minutes.
Preheat the oven to 315℉. Line a baking sheet with a silicone mat.
Take out one portion of the frozen dough out of the freezer and remove the top layer of the paper. Use a tart ring to cut out 5 circles. With the help of a small offset spatula, remove each circle of dough from the parchment paper and line a tart ring on the prepared baking sheet.
Gently press any dough scraps together, wrap in cling wrap, and chill in the fridge. Place the baking sheet in the fridge while you work with the next portion of dough.
Take out the second portion of the frozen dough out of the freezer and remove the top layer of the paper. Cut the dough into strips that are long enough to line the tart rings (about 10 inches) and wide enough to be taller than the tart ring (about 1 inch).
Take the baking sheet with the tart rings out of the fridge. Working quickly and carefully, use a small offset spatula to remove a strip of dough from the paper and line the inside of the tart ring. Gently press the two pieces of dough together to seal the seam together.
Gently press any dough scraps together, wrap in cling wrap, and chill in the fridge. Place the baking sheet back in the fridge for 10 minutes.
Double check that the tart dough is adhered to the sides of the tart ring and the seam is sealed. Use a sharp knife to trim off the excess dough that extends above the ring. Gently press any dough scraps together, wrap in cling wrap, and chill in the fridge.
Use a fork to poke a bunch of small holes in the bottom of the tart. This will prevent the tart shell from puffing up when they bake.
Place the baking sheet in the fridge again for 15 minutes.
Bake until a light golden brown, about 30 minutes. If your dough ended up thinner than mine, you could need as little as 20 minutes, and if it's thicker it could take 35 minutes. Keep an eye on the tart shells.
Once baked, cool 15 minutes before removing the tart rings. Transfer to a cooling rack to cool completely. If not using within the hour, place the tart shells in an airtight container for up to a day before filling.