Heat oven to 325°F with racks in the upper-middle and lower-middle positions.
In a bowl mix sugars and butter, either by hand or with a hand-held mixer until smooth and incorporated. Add in egg and egg yolk, and vanilla extract. Mix until incorporated. Then add in dry ingredients, white chocolate and sour cherries. Mix until incorporated.
Scoop out ¼ cup of dough, roll in a ball, using fingertips, pull apart into two equal halves. Rotate 90 degrees and lightly smoosh back together, with the rough edges on top. Place formed dough ball on one of two parchment-lined cookie sheet, about 9 per sheet. Bake for 18 minutes or until edges are slightly golden and middles are still soft. Let cool for 20 to 30 minutes.
While cookies are cooling, mix all filling ingredients with handheld mixer until whipped and light. About 3 minutes.
Smear about 1 to 2 tablespoons of filling onto bottom side of cookie. Place another cookie, bottom-side down on to filling. Repeat with remaining cookies, cut in half and serve.
Makes 12 individual cookies, 6 large sandwiches, and 12 perfect sandwich-halves.