Prepare the baking sheets and oven: Line three baking sheets with parchment paper so the cookies release easily. Preheat your oven to 350°F (180°C) so it is ready by the time your dough is prepared.
Cream the butter, cream cheese, and sugars: In the bowl of a stand mixer (or with a hand mixer), beat together the butter, cream cheese, granulated sugar, brown sugar, and molasses on low speed for about 3 minutes. The mixture should look light and fluffy. Scrape down the sides of the bowl to ensure even mixing. This step builds air into the dough, creating a soft cookie.
Add the wet ingredients: Mix in the egg, the extra yolk, and the vanilla extract. Blend until smooth. Scrape down the bowl again to make sure everything is fully incorporated. The extra yolk adds richness and helps keep the cookies chewy.
Incorporate the dry ingredients: Gently mix in the flour, baking powder, cream of tartar, and salt until just combined. Avoid over-mixing at this stage, as it can make the cookies dense instead of tender.
Prepare the cinnamon sugar coating: In a small bowl, stir together the cane sugar and ground cinnamon. This will create the classic snickerdoodle exterior.
Shape and fill the cookies: Scoop dough into balls about 2 tablespoons each. Roll each ball in the cinnamon sugar mixture until evenly coated. Place the coated dough balls onto the prepared baking sheet, leaving 2 to 3 inches of space between them. Using the back of a round tablespoon, press a shallow indent into the center of each ball. Spoon about ½ tablespoon of apple butter into the indent, then sprinkle the filling with turbinado sugar for sparkle and crunch.
Bake and cool: Bake the cookies for 8 to 12 minutes, or until the edges are just set but the centers still look soft. The cookies will continue to set as they cool. Let the baking sheet rest on a wire rack until completely cooled before removing the cookies. This prevents the centers from breaking.