1. Preheat oven to 375 degrees. Core and cut apple into small cubes (you want about 1½ cups total). Lightly coat apple with oil and 1 teaspoon of the granulated sugar, then roast in oven until golden brown and cooked through, about 3 to 5 minutes. Set aside to cool.
2. Make the cookies: Reduce oven to 325 degrees. In the bowl of a stand mixer fitted with paddle attachment, beat butter until creamy. Add both sugars and lightly beat again until smooth and incorporated. Scrape down sides of bowl and, with the mixer on low speed, add eggs one at a time, scraping down sides and bottom of bowl with a spatula after each addition. Add vanilla paste and beat until combined.
3. In a medium bowl, combine flour, baking soda, spices, and oats. Add flour mixture to butter mixture in two separate batches, mixing well between each addition. When a dough has formed, add raisins, pecans, and cooled roasted apples, mixing just enough to incorporate.
4. Scoop dough into 2-inch balls and arrange on a parchment-lined baking sheet, gently pressing down on each. Bake for about 10 minutes, rotating halfway through. Transfer cookies to a wire rack and allow them to cool completely.
5. While cookies cool, make the icing: In the bowl of a stand mixer fitted with paddle attachment, beat butter until pale in color. Scrape down sides of bowl. Add cream cheese and beat until light and fluffy. Scrape down sides of bowl again.
6. In a medium bowl, combine remaining ingredients. With mixer on low speed, add powdered sugar mixture in batches and slowly beat until smooth and creamy.
7. Transfer filling to a piping bag and let chill in refrigerator for 15 minutes before proceeding with recipe.
8. Assemble the cookies: On the flat side of one cookie, pipe a ring of cream cheese icing around the edge, leaving room for 1 to 2 tablespoons of apple butter in the center. Fill center with apple butter. Gently press flat side of a second cookie to the filling, forming a sandwich. Repeat with remaining cookies and filling.