In a medium-sized bowl, whisk together the flour, baking soda, salt, cinnamon and nutmeg until well blended.
In a large bowl, beat the butter, brown sugar and granulated sugar, with an electric mixer at medium speed, or by hand, until light and fluffy. Beat in the egg, egg yolk and vanilla extract, one at a time, until well blended. Stir in the flour mixture just until combined. Stir in the cooled apples and 3/4 cup of the candied walnuts.
If your dough is soft, chill it in the refrigerator until it's easier to work with, about 15-20 minutes. Divide the dough into 14 equal golf ball-size portions, about 1 1/2 oz (43g) each. Roll them into balls and chill in the refrigerator for 1 hour.
Preheat the oven to 350ºF (180ºC). Line 2 large cookie sheets with parchment paper. Place the dough balls at least 3 inches apart onto the cookies sheets. Top with candied walnut halves.
Bake until the tops of the cookies are set and the edges are golden brown, about 12-14 minutes. The cookies will spread a bit. Remove the cookies from the oven. Immediately use a large round cookie cutter to shape the hot cookies by sliding it around each one in a circular motion a couple of times. Cool on the cookie sheet for 3 minutes, then transfer to a cooling rack.