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