Vanilla Bean Shortbread Cookies with Vanilla Bean Glaze

1 In a large bowl, cream together the softened butter and sugar until light and fluffy using a hand (or stand) mixer.
2 Add the caviar from the split vanilla bean, vanilla extract and milk. Combine with the butter and sugar mixture until smooth and well incorporated.
3 Sift together the flour and salt, then add to the wet ingredients, mixing until the batter just comes together. (Mine was a little bit crumbly, and that's OK. To check and make sure that yours will form into balls for the next step, just grab a little piece of the dough and press it together in your hand. If it forms a ball without falling apart, you're good to go. If it doesn't, add an additional tablespoon of milk until it does this.)
4 Cover with plastic wrap and let chill in the refrigerator for at least an hour.
5 While the dough is chilling, make the Glaze.
6 Combine the powdered sugar, the rest of the caviar from the vanilla bean, the vanilla extract and milk in a smaller bowl, whisking until smooth. Set aside.
7 Once your dough has finished chilling, preheat the oven to 350°F.
8 On a parchment-paper lined baking sheet, scoop out 1" rounds of the dough, placing evenly on the baking sheet. Using a fork, flatten the tops of the cookies using criss-cross marks.
9 Bake the cookies for 15-20 minutes (or until slightly browned and crisp).
10 Let cool on a wire rack, then drizzle with the glaze and enjoy!