Add unsalted butter, light brown sugar and granulated sugar to stand mixer. Cream butter and sugar until smooth and creamy, about 3 minutes. Scrape down sides of bowl, if necessary.
Add egg, molasses, apple butter, and vanilla bean paste to sugar mixture. Beat on low until fully incorporated, about 1 minute.
Add all-purpose flour, baking soda, ground cinnamon, fine sea salt, ground ginger, ground cloves, and ground nutmeg to large mixing bowl. Whisk to combine.
Add old-fashioned oats and chopped walnuts to flour mixture. Stir to combine.
Add the sugar mixture to the flour mixture. Fold in with large spatula.
Add grated apple and fold in with large spatula.
Cover cookie dough with plastic wrap and chill at least 4 hours and up to 2 days.
Preheat the oven to 350 degrees F. Line 2 cookie sheets with parchment paper.
Roll about 2 tablespoons cold cookie dough into a ball. Place on prepared cookie sheets, 9 to a sheet 3-inches apart. Do not press down. Top each cookie dough ball with diced apple and white chocolate chips.
Chill remaining dough.
Bake in hot oven for 12 to 13 minutes. Cool on wire rack.
Repeat process with remaining cookie dough.
Store cookies in airtight container.