In a food processor or large mixing bowl, combine the flour, sea salt, and sugar.
Add the cold butter and pulse until the mixture becomes crumbly with pea sized pieces of butter remaining. If mixing by hand, use a pastry cutter.
Add the sourdough starter and vinegar. Mix just until the dough comes together. If needed, add cold water one teaspoon at a time until the dough holds together when pressed.
Turn the dough onto a work surface and gently press it into a rectangle.
Wrap tightly and refrigerate for at least 1 hour or up to 2 days.
Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
Generously flour your work surface and roll the chilled dough into a rectangle approximately 10 inches by 16 inches and about ⅛ inch thick.
Trim the edges and reserve the scraps for mini pop-tarts.
Cut the dough into four strips approximately 10 x 4 inches each.
Brush egg wash around the outer edges of one strip.
Place about 2 tablespoons of filling on one half of the strip, leaving a small border around the edges.
Fold the empty half over the filling and seal the edges with a fork.
Transfer to the prepared baking sheet and repeat with the remaining strips.
Brush the tops with the remaining egg wash.
Bake for 25 to 30 minutes, or until lightly golden brown.
Allow the pop-tarts to cool completely before icing.
To make the icing, whisk together the powdered sugar, almond extract, sea salt, and 1 teaspoon water.
Add additional water as needed until the icing is thick but spreadable.
Spread over the cooled pop-tarts and allow the icing to set before serving.