Melt-in-Your-Mouth Orange Cookies with Cranberries and Orange Frosting

mashed cooked carrots (about 7 ounces uncooked—4 to 5 large carrots or 16 larger baby carrots)

unsalted butter, at room temperature*

vegetable shortening*

granulated sugar

large eggs, at room temperature

Zest of 2 large oranges

freshly squeezed orange juice

pure vanilla extract

all purpose flour

whole wheat pastry flour or white whole wheat flour

baking soda

kosher salt

roughly chopped reduced-sugar dried cranberries

powdered sugar

unsalted butter, softened to room temperature

freshly squeezed orange juice

pure vanilla extract