In the bowl of a stand mixer with a paddle attachment, add butter and sugar. Mix until light and creamy. (You could also use a handheld mixer.)
Add the egg, cherry juice, and almond extract. Mix until incorporated.
In a separate bowl add flour, baking soda, and cream of tartar. Whisk together to combine.
With the mixer on low, add the flour mixture to the wet ingredients, 1 cup at a time, until combined.
Gently fold in the cherries and the almonds.
Add dough to a sheet of parchment paper and roll into 2, 8-inch rolls. Wrap in plastic wrap and seal the ends. Place the dough in the refrigerator to chill for about 2 hours, or until firm.
When ready, preheat the oven to 375°F and line 2 large baking sheets with parchment paper.
Remove the dough from the refrigerator and place each roll on a cutting board.
Slice each dough log into ¼-inch cookies and place cookies onto the prepared baking sheets about 2 inches apart.
Bake 7-9 minutes, or until edges are slightly browned.