Prepare a baking sheet by lining it with parchment paper; if you don't have any, use an ungreased baking sheet.
Coarsely chop the fresh cranberries using a food processor or a sharp knife; set them aside.
In a large mixing bowl or the bowl of a stand mixer, beat together the butter, powdered sugar, vanilla extract, and almond extract until light and fluffy, about 2 minutes.
Add the all-purpose flour and mix with clean hands just until combined.
Gently fold in the chopped cranberries and orange zest.
Divide the dough into three equal portions and roll each into a log shape; wrap in plastic wrap and refrigerate for 30 minutes.
Unwrap the dough and slice cookies into 1/4-inch thick slices using a sharp knife.
Dip the top and roll the sides of the cookies in a small bowl with the 3 tablespoons granulated sugar.
Place unbaked cookies on the prepared baking sheet, 2 inches apart.
Bake in a 300°F (150°C) oven for 17 to 20 minutes; the bottom of the cookies will be light golden brown when done.
Cool on a wire rack and enjoy!