If using a food processor: Combine the flour, sugar, salt, and baking powder in the bowl of a food processor fitted with the metal blade. Pulse a few times to combine.
Add the pieces of cold butter and pulse until the mixture is crumbly, with lots of pea-sized clumps of butter within. This will create a flaky texture.
Pour in the ice cold water and pulse until the mixture is evenly moistened and very crumbly. You want it just wet enough to hold together.
Dump the dough crumbles onto a work surface and divide into two even piles. Make two balls of dough and pat each one into a 5-inch disc.
Wrap the discs in plastic wrap and refrigerate for at least 45 minutes and up to 3 days. Chilling the dough helps it to relax and makes rolling easier.
If making by hand: In a large mixing bowl, whisk together the flour, sugar, salt, and baking powder. This helps evenly distribute the dry ingredients.
Add the butter cubes and use a pastry cutter or two knives to cut the butter into the dry ingredients until the mixture resembles coarse crumbs. You want to see bits of butter for the best texture.
Gradually add the ice cold water, mixing with a fork, and then your hands until the dough comes together into a ball.
Divide the dough in half, shape into disks, wrap in plastic wrap, and refrigerate for at least 45 minutes and up to 3 days.
In a large bowl, combine the pitted cherries, lemon juice, almond extract, sugar, salt, and tapioca flour. Toss until combined; don’t worry if the mixture is powdery—this is normal!
Preheat the oven to 425°F and set an oven rack in the lower third position. Line a baking sheet with aluminum foil to catch any juices that may bubble over.
Prepare the bottom crust: Remove one disc of dough from the refrigerator. Lightly dust a clean work surface with flour and place the dough on it; sprinkle a bit of flour over the dough as well. Gently knead the dough with your hands just until it becomes soft and malleable.
Roll the dough out into a 14-inch circle, adding more flour as needed to prevent sticking. Carefully lift the dough by draping it over your rolling pin and transfer it to a 9-inch deep-dish pie pan.
Gently press the dough into the pan, making sure to ease it into place without stretching. Trim the edges of the dough to extend about ½ inch beyond the pie pan's lip.
Fill the pie: Transfer the filling into the crust and press it into an even layer (do not mound). Dot the cherries with the remaining butter. Refrigerate while you prepare the top crust.
Prepare the lattice top crust: Remove the top disc of dough from the refrigerator and roll it out into a 10×15-inch rectangle. Use a pizza or pastry cutter to trim the edges and cut the dough into 14 one-inch-wide strips.
Retrieve the filled pie from the refrigerator. Lay half of the strips horizontally over the pie filling, leaving about ½ inch of space between each strip.
Fold back every other strip halfway over itself. Place one strip of dough vertically over the unfolded strips.
Unfold the folded strips over the new strip, then fold back the alternating strips that were previously left unfolded.
Lay another strip of dough parallel to the first vertical strip, about ½ inch away from it. Repeat the process, folding back the strips as necessary, until the lattice crust covers the entire pie.
Trim any excess dough from the edges of the lattice strips, leaving a slight overhang. Fold the edges of the bottom crust over the lattice strips, then crimp or flute the edges to seal the pie.
Place the pie on the lined baking sheet and bake at 425°F for 20 minutes. Reduce the oven temperature to 375°F and continue baking for an additional 60 to 70 minutes.
The pie is done when the crust is golden brown and the filling is bubbling both on the edges and in the center (if you have a digital thermometer, it should be at least 213°F in the center).
Keep an eye on the pie during the second half of baking and tent lightly with foil if it’s getting too brown on top.
Immediately move the hot pie off the foil and place it on a heat-proof surface. If necessary, take a wad of wet paper towels and wipe any cherry juice from the edges.
Let the pie cool completely before slicing, at least 8 hours or overnight. Resist the temptation to cut into the pie while it’s even slightly warm, or you will end up with cherry soup!
Once cooled, you can keep the pie at room temperature for up to 2 days, covering it loosely with foil to prevent it from drying out. If you need to store the pie for longer than 2 days, place it in the refrigerator, covered with plastic wrap or aluminum foil, and store for up to 4 days.