For the galette: Position a rack in the center and preheat the oven to 375 degrees F. Melt the butter in a large nonstick skillet over medium-high heat. Add the apples and sprinkle with the salt. Saute until almost tender, tossing occasionally, about 10 minutes. Remove the skillet from the heat. Whisk the sugar, spices and arrowroot in a small bowl until no cornstarch lumps remain. Sprinkle the spiced sugar and lemon juice over the apples in skillet, and toss to blend. Cool to lukewarm.
Place a large sheet of parchment paper on the work surface. Unfold the pastry sheet on the parchment and sprinkle both sides lightly with flour. Roll out the pastry to 12-inch square, lifting, turning and sprinkling with more flour to keep from sticking. Cut off the corners (with a rounded cut), making a 12-inch-diameter pastry round.
Brush the pastry all over with some beaten egg. Starting 2 inches in from the edge (to leave wide border), arrange the apple wedges close together in a circle on the pastry. Arrange the remaining apples in a smaller circle in center (ends may overlap first ring of apples). Fold the pastry border partially over the filling, pleating the pastry in loose folds. Brush the folded-up pastry border with some beaten egg. Slide the galette with the parchment onto a heavy baking sheet. Scrape the juices from the skillet over the apples. Bake galette until pastry edge is deep golden brown, 30 to 35 minutes.
Meanwhile, make the topping: Toss the goat cheese, almonds and cherries in a medium bowl until evenly distributed (the cheese should remain in distinct pieces). Chill until ready to use.
Remove the galette from the oven. Sprinkle the topping evenly over the filling. Return the galette to the oven and bake for 5 minutes longer to soften the cheese and cherries. Cool 20 minutes and serve warm, or cool for 2 hours to serve at room temperature.
Recipe courtesy of Giada De Laurentiis