Step 1Combine the dates, butter, brown sugar and cinnamon in a food processor or mixer. Process until smooth. Remove the date butter to a small bowl and refrigerate until somewhat firm.
Step 1Place the flour, sugar and salt in the bowl of a food processor. Pulse to mix. Add the cold butter all at once and pulse a few times until the butter and flour form crumbs. Start adding ice water, a tablespoon at a time, pulsing each time. Use as much water as needed for the dough to hold together when a clump is gently pressed between your fingers. The dough will be quite loose in the processor. Dump the dough out onto a large piece of plastic wrap. Gather the dough together using the plastic wrap and force it into a flattened round. Chill the dough an hour or longer before rolling out.
Step 1Heat the oven to 400 degrees. Set out a small bowl of water and a pastry brush. Divide the pastry dough in half. On a lightly floured surface, roll out half the dough about 1/8-inch thick into a rough square shape. Trim the dough to make a 12-inch square; set the trimmings aside. Cut the square into 4 (6-inch) squares. Take each square and make a cut from each corner halfway to the center of the square. Repeat with the second half of the dough. You will have 8 (6-inch) squares.
Step 2Use a melon baller to remove the core of each apple half. Fill the cavity of each apple half with a mound of the date butter. Place each apple half, core side down, on the center of a dough square. Brush the corners of the dough lightly with water. Fold each corner into the center and press together to seal. Place the dumplings on a parchment-lined baking sheet.
Step 3Reroll the pastry trimmings, if you'd like, and cut out 8 leaves using a small knife or cutter. Place one on each dumpling, fixing it on with a brush dipped in a little water.
Step 4Beat the egg yolk lightly with the cream. Brush each dumpling with egg wash. In another small bowl, mix the sugar and cinnamon and sprinkle 1 or 2 teaspoons on each dumpling. Bake the dumplings until the pastry is golden and the apples feel tender when pierced with a knife, about 25 minutes; rotate the baking sheet halfway through. Place the dumplings on plates and spoon warm maple sauce over and around them.
Step 1Bring the water and cinnamon stick to a boil in a small saucepan over high heat.
Step 2Combine the brown sugar and the cornstarch in a small bowl and add to the boiling water. Lower the heat and simmer, whisking occasionally until slightly thickened, about 5 minutes. Remove from the heat and add the syrup and butter, stirring until the butter melts. Remove the cinnamon stick before serving. Serve warm.