Pulse the flour, cocoa powder, sugar, and salt together in your food processor. Scatter the cold, cubed butter over the top and pulse again until the mixture looks like coarse crumbs. A few visible butter pieces are fine here, they help create flaky layers once baked.
Add the sour cream and pulse until the dough starts clinging together in small clumps. It should hold its shape when you press it between two fingers. Transfer it to plastic wrap, flatten it into a disk, and chill for 30-60 minutes.
While the dough chills, melt the chocolate chips, salted butter, and heavy cream together in short bursts in the microwave. Stir in the vanilla and powdered sugar once smooth. Set the filling aside so it can cool and thicken before you use it.
Once chilled, roll the dough out on a lightly floured surface to about ⅛ to ¼ inch thick. Cut it into rectangles roughly 2.5 by 4 inches. You should get enough for about 10 pop tarts, with a little dough left for scraps.
Brush one rectangle with egg wash, then spoon a rounded teaspoon of the cooled filling into the center. Top with a second rectangle and press the edges together. Crimp all four sides firmly with a fork so nothing leaks out during baking.
Poke 6-8 small holes across the top of each pop tart with a toothpick so steam can escape while baking. Bake at 400°F for 15-17 minutes, until the crust is set and slightly firm to the touch. Let them cool fully on the pan before glazing.
Whisk together the powdered sugar, cocoa powder, milk, corn syrup, and vanilla until smooth and glossy. Spoon it over each cooled pop tart, letting it drip slightly down the sides. Add sprinkles right away, before the glaze sets.