A triple dose of cream cheese (mixed into the batter, in chunks in the dough and as a glaze on top) makes these pillowy cookies extra tangy. Freezing the cream cheese before stirring it into the dough makes it easier to cut into clean pieces and keeps the chunks from disintegrating when shaping the dough into balls.
Position an oven rack in the center of the oven and preheat to 325 degrees F. Line a baking sheet with parchment.
Combine the butter, vanilla, 4 ounces of the room-temperature cream cheese and 1 teaspoon of the salt in a large bowl and beat with an electric mixer on medium speed until creamy, about 1 minute. Add 2 cups of the sugar and beat until pale and fluffy, about 3 minutes. Add the egg yolk and beat until smooth, then add the flour and beat on low until the dough just comes together. Remove the frozen cream cheese from the freezer and chop into 1/4-inch cubes. Add the cubes to the dough, quickly stirring with a rubber spatula to evenly incorporate them into the dough. Refrigerate the dough for 1 hour.
Using a 1-ounce ice cream scoop or 2 tablespoons, scoop 12 portions of dough, roll into balls and transfer to the prepared baking sheet, spacing them evenly apart. Lightly flour the bottom of a 1/2-cup measuring cup and use it to flatten each cookie into a disk about 1/2 inch thick, re-flouring the cup after each cookie.
Bake, rotating the baking sheet halfway through, until the cookies look set but are still pale and barely brown on the bottom, 20 to 24 minutes. Cool the cookies on the baking sheet for 1 minute, then transfer them to a wire rack to cool completely. Repeat with the remaining cookie dough.
Meanwhile, combine the remaining 2 ounces room-temperature cream cheese, 2 cups sugar and 1/4 teaspoon salt in a medium bowl and beat with an electric mixer on low speed until the mixture forms a thick paste. Add the milk and stir slowly until a thick glaze forms.
When the cookies are cool, dip the entire surface of the top of each cookie in the glaze and lift up, letting the excess glaze drip off, then flip the cookie right-side up and onto the cooling rack. If the glaze is too thick, add another teaspoon of milk to loosen it. If using the cranberries or lime zest, sprinkle on top of the cookies while the glaze is still wet. Allow the glaze to set before serving, at least 10 minutes. Store the cookies in a single layer in an airtight container for up to 5 days.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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