For the cookies: Preheat the oven to 325 degrees F, with racks in the upper and lower thirds of the oven. Line two rimmed baking sheets with parchment paper and set aside.
Mix the flour, baking soda and salt in a small bowl until combined. In the bowl of a stand mixer, beat the butter and both sugars on medium speed until smooth and incorporated.
Add the vanilla, egg and egg yolk and mix until incorporated. Then add the flour mixture, sour cherries and white chocolate.
Mix until incorporated.
Scoop a level tablespoon of dough, roll in a ball and, using fingertips, pull apart into two equal pieces. (You'll have 36 to make 18 sandwiches.)
Place the formed dough balls on one of the prepared baking sheets, about 2 inches apart.
Bake until the edges are slightly golden and the middles are still soft but not wet, 12 to 15 minutes.
Let the cookies cool for 20 to 30 minutes on the baking sheets.
For the filling: While the cookies are cooling, beat the almond butter, confectioners' sugar, butter and salt with a hand-held mixer until whipped and light, about 2 minutes. Chill the filling until ready to assemble the cookies.
Spread 1 tablespoon of the filling onto the bottom side of a cookie.
Place another cookie, bottom-side down, onto the filling. Repeat with the remaining cookies.
