Step 1In a large skillet over a medium flame add the butter, vanilla bean and seeds, cook until the butter turns golden brown, about 6 minutes. Add the apples, letting them caramelize on one side, then turn, about 5 minutes total.
Step 2Sprinkle the sugar and brown sugar over the apples and cook, turning occasionally to caramelize and soften the fruit, about 10 minutes. Add the heavy cream and continue to cook for 1 minute. Remove from heat. Remove the vanilla bean and put the apple mixture in a food processor, add lemon juice and pulse until smooth. Cool over ice, 45 minutes to 1 hour. (This can be made and stored in an airtight container in the refrigerator for 1 week.)
Step 1Line two 17-by-12-inch baking sheets with parchment paper and set aside. In a food processor, blend the almond flour, powdered sugar, ginger and cinnamon for 1 minute. Sift the blended almond mixture directly into a medium mixing bowl. Set aside. (This can be made up to 2 days in advance.)
Step 2Fill a small saucepan halfway with water. Bring to a simmer, then remove from the heat. In the bowl of a stand mixer, whisk the egg whites until foamy. Place the bowl over the pot of hot water and whisk quickly until the egg whites reach 100 degrees on a candy thermometer.
Step 3Remove the bowl from the pot of water and whisk in the cream of tartar. Place it on a stand mixer fitted with the whip attachment. Whip on medium speed for 2 minutes, then gradually beat in the sugar. Continue whipping for 6 minutes until the egg whites come to medium stiff peaks and are shiny.
Step 4Turn the mixer to the lowest setting and carefully spoon in the molasses. Remove the bowl from the mixer. Add egg whites to the almond mixture by gently bringing the flat side of a rubber spatula through the center of the egg whites and up the opposite side of the bowl, folding the dry ingredients over the egg whites. Repeat the same motion 50 times, turning the bowl a quarter turn each time.
Step 5Fit a pastry bag with a medium round tip (No. 4) and fill with the mixture. On the parchment-lined baking sheets, pipe 1-inch rounds (the batter will be slightly wet) by holding the bag at a slight angle and releasing small amounts of batter. Allow one-half inch between cookies; they will spread slightly. Keep the piped cookies at room temperature, uncovered, for 1 to 2 hours. (This will help form a skin.)
Step 6Heat the oven to 325 degrees, placing the racks in the center and lower shelves of the oven.
Step 7Bake the macarons for 12 minutes, reverse the trays on the racks and rotate. Bake 12 to 14 minutes more, or until firm and not wet. Cool on a rack.
Step 8Fill the macarons by placing the apple compote in a pastry bag fitted with a small round tip. Pipe a one-half-inch round of filling on to the bottom (flat side) of one cookie, then place another cookie on top to make a sandwich (try to pick two cookies the same size and shape). Twist gently to spread the filling. These are best filled 1 hour before eating so that the apple compote makes the macaron melt in your mouth.