To make the pie crust, add the flour, cocoa powder, sugar, and salt to the bowl of a food processor. Pulse for a few seconds until well combined.
Add the cubed butter and process until the mixture resembles coarse sand.
Add the cold water and pulse until the dough comes together.
Place the dough on a clean surface and knead gently until smooth, then form into a disc and wrap in plastic wrap. Refrigerate for at least 1 hour.
Meanwhile, make the filling: Whisk together the pomegranate juice and flour until no clumps remain.
Add the pomegranate juice mixture, cherries, sugar, sweetened condensed milk, vanilla extract, and salt to a large saucepan.
Bring to a boil, then reduce heat to a simmer and cook until the cherries begin to break down and the mixture begins to thicken, about 10 minutes. Remove from heat and allow to cool completely.
Preheat the oven to 375 F.
Once the pie dough has chilled, divide it into 2 halves. Roll the first half out on a lightly floured surface until it is large enough to fit a 9-inch standard pie pan (not deep dish).
Place the dough into the bottom of the pie pan. Spoon the cherry filling over the dough.
Roll out the second dough half on a lightly floured surface and cut into 1 inch-wide strips.
Place the strips on top of the pie filling, creating a lattice pattern.
Press or crimp the edges of the pie crust together.
Place the pie on a baking sheet and bake for 40-45 minutes, until the filling is bubbly and the crust has browned.
Transfer the pie to a wire cooling rack and cool completely before slicing.