Make the Dough
In a large bowl, combine the flour, salt, powdered sugar, and baking powder.
Add the cold butter cubes and rub them into the flour mixture with your fingertips until the mixture resembles fine crumbs.
Add the egg and sour cream.
Quickly knead until a smooth, elastic dough forms.
Wrap the dough tightly in plastic wrap and refrigerate for 30–40 minutes, or preferably overnight for the best texture.
Make the Apricot Filling
Place the apricot halves and sugar in a saucepan.
Cook over low heat for about 5 minutes, until the apricots begin releasing their juices.
Dissolve the cornstarch in 3 tablespoons of water.
Stir the cornstarch mixture into the apricots and bring to a gentle boil.
Cook for 3–5 minutes, stirring occasionally, until slightly thickened.
Remove from the heat and allow the filling to cool completely before assembling the pie.
Assemble the Pie
Preheat the oven to 350°F (175°C).
Divide the chilled dough into two portions, one slightly larger than the other.
Roll out the larger portion and fit it into a 9-inch pie dish or similar baking pan.
Spoon the cooled apricot filling evenly over the crust.
Roll out the remaining dough and cut it into approximately 1/2-inch-wide strips.
Arrange the strips in a lattice pattern over the filling. For a decorative finish, braid some of the strips if desired.
Lightly sprinkle the top with granulated sugar.
Bake the Pie
Bake for 40–45 minutes, or until the crust is golden brown.
After about 25 minutes, loosely cover the pie with aluminum foil if the crust is browning too quickly.
Remove from the oven and allow the pie to cool for at least 20–30 minutes before slicing and serving.