Prepare the Brown Sugar-Cinnamon Filling: In a medium bowl, whisk together the brown sugar, cinnamon, and flour.
Prepare the Strawberry Filling: In a small bowl, whisk together the cornstarch and water, and then combine with the jam in a small saucepan over medium heat. Bring to a boil and simmer for 2 minutes, stirring frequently. Remove from the heat and let cool.
Make the Pastry Crust: In a large bowl, whisk together the flour, sugar, and salt. Using a pastry blender, cut in the butter until it is the size of peas and the mixture holds together when you squeeze it. In a small bowl, whisk together the egg and milk and add to the dough. Mix together with a fork until everything is evenly moistened. Knead briefly on a floured surface, if necessary, until the dough comes together.
Divide the dough in half. (At this point you can wrap each in plastic wrap and refrigerate for up to 2 days. If you refrigerate the dough, let it come to room temperature for about 15 minutes before rolling out.) Roll out one piece of dough to about ⅛-inch thick, in a 9½ by 12½ rectangle. Using a sharp knife, pastry wheel or bench scraper, trim the rectangle to 9x12 inches. Cut the sheet of dough into nine 3x4-inch rectangles. Using a spatula, transfer the rectangles to a baking sheet that has been lined with parchment paper or a silicone baking mat.
Assemble the Pastries: In a small bowl, whisk together the egg and milk. Brush the egg wash on each of the rectangles. Spoon a tablespoon of filling into the center of each rectangle, leaving a ½-inch of space around the edges.
Make the Icing: In a small bowl, whisk together the powdered sugar, milk, cinnamon (if using), and vanilla extract. The icing should have a very thick, but still spreadable, consistency. If necessary, add a splash of milk at a time, until that consistency is reached. Spread a spoonful of icing over top of each pastry and allow to sit for at least 30 minutes so the icing can set.
Nutritional values are based on one serving