Beat the butter, sugar, and salt together in a medium bowl or a stand mixer. Add the orange zest, vanilla extract, and juice. Stir in the flour/baking powder mixture.
Divide the dough into two pieces and form into logs. Wrap each piece in plastic wrap. Refrigerate for at least 30 minutes.
When ready to bake, preheat oven to 350F degrees with two racks in place in the middle of the oven. Grease two baking sheets or line with parchment paper. Chop the cranberries finely and place in a bowl. Also measure 1/4 cup of sugar and place in a second bowl.
Take the dough out from the refrigerator and remove the plastic wrap. Divide dough into 48 similarly sized pieces. Shape dough into balls and place on the prepared baking sheet about 3 inches apart. Flatten each ball with your thumb and sprinkle with cranberries. Then dip the base of a glass into the bowl of sugar. Press the cookie flat with the glass until about 1/8-inch thick. If a cookie stick to the glass, use a knife or metal spatula to remove it and flatten it again with a glass dipped in sugar.
Bake the cookies in a 350F degree oven for about 7 minutes, then reverse the pans (so the pan on the upper oven rack goes to the lower rack, and the pan on the lower rack goes to the upper rack). Cookies are done when they turn golden brown around the edges—around 14-15 minutes of total bake time. Cool the cookies for a minute on the baking sheet and then transfer to a rack. Repeat with the second batch of dough and enjoy!