Pulse the flour, sugar, and salt together in a food processor, then scatter in the cold, cubed butter and pulse until the mixture looks like coarse crumbs with pea-sized bits remaining. Add the sour cream and pulse just until the dough starts clumping together. Turn it out, shape it into a disc, wrap it, and chill it for 30 to 60 minutes while you prepare the filling.
Whisk the sugar and cornstarch together in a small saucepan, then stir in the quartered strawberries and lemon juice. Cook over medium heat, mashing the berries as they soften, until the mixture thickens into a jammy consistency. Remove it from the heat, stir in the butter, and let the filling cool completely before you use it.
Once the dough has chilled and the filling has cooled, roll the dough out on a floured surface to about a quarter-inch thick. Cut it into even rectangles using a knife, pizza wheel, or cookie cutter. You'll want an even number so each pop tart gets a top and a bottom piece.
Brush one rectangle with egg wash, then spoon a rounded tablespoon of strawberry filling into the center. Top with a second rectangle, then crimp the edges with a fork to seal everything in tightly. Brush the top with more egg wash and poke a few holes so steam can escape while baking.
Arrange the assembled pop tarts on a parchment-lined baking sheet and bake at 400°F until they're golden brown, about 15 to 17 minutes. Let them cool completely on the pan before you even think about icing them, or the glaze will just slide right off.
Whisk together the powdered sugar, milk, corn syrup, and vanilla until smooth and glossy. Drizzle it generously over each cooled pop tart, then finish with sprinkles while the icing is still wet so they actually stick.