Preheat the oven to 325 degrees.
Beat the butter and sugar together until light and fluffy. Add the egg and extract and mix in well.
Mix together the flour, salt and graham cracker crumbs in a separate bowl, then slowly add to the butter mixture.
Line a baking sheet with parchment paper and roll heaping teaspoons (mine are close to 1½ teaspoons) into balls. Roll each ball in a bowl filled with graham cracker crumbs. Place the balls on the baking sheet and press down on the center of each cookie with your thumb or back of a spoon. Chill for about 10 minutes.
Mix together the diced apples, sugar, cinnamon, extract and cornstarch together. Bake in the oven for about 15 minutes. I put them in a cast iron skillet, but an 8x8 baking pan would work, too. The apples should be semi-soft, but not too soft. Set aside.