Preheat oven to 375 degrees F. Line a rimmed baking sheet with parchment paper.
Prepare the apricot filling by placing the sliced apricots in a large bowl and adding the sugar, cornstarch, and salt. Stir to combine, then set aside.
To prepare the crust, mix the flour and salt in a large bowl. Cut in the butter with a fork or pastry cutter until well combined. The mixture should resemble wet sand.
Add cold water 1 Tbsp at a time and mix with a wooden spoon until it forms a loose dough. It should be moist enough to form into a ball, but not too sticky to knead. Add more flour if it gets too wet.
Turn onto a well-floured surface, shape into a disc, and use a rolling pin to roll into a large circle, adding more flour as needed.
Place a small dish that is about 4 inches across (or a large round cookie cutter) over the dough and use a knife or pizza cutter to cut out circles. It makes 9 or 10. Re-form the dough scraps and roll back until all the dough is used.
Use a slotted spoon to scoop modest amounts of filling on one half of each pie circle, leaving excess liquid behind. Then run a wet finger around the edges to help them seal. Use your hands to gently fold the dough over. Use a fork to seal the edges. Repeat until all of the filling is used and all of the pies are on the baking sheet.
Use a toothpick or small knife to poke a few holes in the top of each. Brush the tops of the pies with melted butter or coconut oil and sprinkle the tops with sugar. Bake for 25-35 minutes, or until golden brown.
Let it cool for 5 minutes before serving. Let leftovers cool completely. Store in an airtight container at room temperature for up to 3 days. Best when fresh. (I doubt there will be any leftovers!)