Prepare the grill for indirect cooking over medium heat, as close to (350°F) as possible. Place the stone over indirect medium heat, close the lid, and preheat for at least 10 minutes.
Peel, halve, and core the apples. Cut the halves lengthwise into 1/4-inch slices and place in a large bowl. Add the sugars, orange juice, cinnamon, and orange zest and stir to thoroughly combine.
Remove the dough from the refrigerator. If using a prepared dough, lay the dough on a piece of parchment. If rolling homemade dough, lightly flour a work surface. Lightly flour a rolling pin and roll out the dough into an 11-inch circle, 1/8 to 1/4-inch thick. Transfer the dough to a piece of parchment. Slide the dough on the parchment onto a rimless baking sheet or pizza peel.
Arrange the apples in a concentric pattern in the center of the dough, leaving a 1 1/2-inch border of uncovered dough around the perimeter. Fold the edges of the dough over the filling, pleating them as needed. Lightly brush the crust with the cream, then sprinkle the entire top evenly with the 1 tablespoon sugar.
Slide the parchment with the galette onto the pizza stone. Grill over indirect medium heat, with the lid closed, until the apples are tender, the juices are bubbling, and the crust is golden brown, 35 to 40 minutes, turning the galette once or twice to ensure even cooking. Using the baking sheet or pizza peel, remove the galette and parchment from the stone. Transfer the galette to a plate or cutting board and let cool for at least 20 minutes. Serve warm or at room temperature with whipped cream.