Add the butter to the bowl of a stand mixer, or in a large bowl with an electric mixer, and beat on medium-high speed for 1-2 minutes, until smooth. Scrape down the sides of the bowl and add the powdered sugar and beat again for 1 minute.

Add the vanilla bean paste and salt and beat until incorporated, scraping down the bottom and sides of the bowl as needed. Add the flour and cornstarch and beat on medium-low until just combined and the dough starts to combine together and pull away from the sides of the bowl. It will seem dry at first, but scrape down the sides of the bowl and continue to beat until it forms a dough. Cover the bowl with plastic wrap and chill for 30 minutes in the refrigerator.

Line a large baking sheet with parchment paper. Generously flour a clean work surface and roll the dough out into 1/4 inch thick. Use a floured round cookie cutter to cut out half of the cookies and a scalloped round cookie cutter and small cookie cutter to cut out the wreaths. Gather the scrapes and re-roll the dough until it’s all gone. Arrange the cookies 1 inch apart on the baking sheet and chill for another 15-30 minutes.

Preheat the oven to 350°F. Bake the cookies for 8-10 minutes, rotating halfway through, until the edges are set and just barely turning golden brown. Allow them to cool for 5 minutes then transfer to a wire rack to cool completely.

To make the icing, whisk the powdered sugar, vanilla, and milk in a shallow dish or bowl until the lumps are gone. Dip the cooled cookies upside down in the icing, being careful that the cookies don’t break when you lift them out.