Place the butter and salt in a bowl and mix for a few minutes until creamy and fluffy, on medium speed (with a hand-held mixer or stand mixer). Make sure to scrape down the sides of the bowl as well.
Add the sugar and mix for a further few minutes on medium speed, until you have a light and fluffy butter-sugar mixture. This can take about a further 4 - 5 minutes. Scrape down the sides of the bowl again.
Add the egg and vanilla, and mix on medium speed until the egg has mixed in with the dough - no more than 1 minute.
In a separate bowl, sift the flour and baking powder together. Add the milk powder and mix.
Add the flour mix to the dough in 2 - 3 additions, while mixing on the lowest speed (or stir speed). Mix only until the flour is incorporated. DO NOT OVER-MIX as this can result in a tough cookie dough.
Use your hands to bring the dough together to form a smooth cookie dough. The dough should be soft and a little sticky, but if it's is too sticky, you can add up to 2 tbsp of flour.
Split the dough into two equal portions and shape each portion into a disc.
Place each disc of dough in a square gallon-size ziploc bag. Then roll out the dough to a 3/16 - 1/4 inch thickness (will be easier to do if the bag isn't closed). Once the dough has been rolled out, close the bag while making there are no trapped air pockets inside. You should end up with two rectangles that are 6 x 10 inches each.
If you don't have ziploc bags, then wrap the dough discs in plastic wrap and chill for a few minutes (about 15 - 30 minutes). Then roll out the dough between two pieces of parchment paper.
Next, place the rolled out dough (that's in a ziploc bag or between parchment paper), on a half sheet pan (or something flat), and transfer it to the fridge to chill.
Once the rolled out dough is chilled, place it on a flat surface that's lightly dusted with flour, and cut out round cookie. You can use scalloped round cookie cutters, or a simple cookie cutter. I used a 2.5 inch round cookie cutter here.
Re-roll the scraps and cut more cookies. You should get about 28 - 30 cookies in total.
Place the cut cookies on a parchment paper-lined half sheet pan and cover with plastic wrap. Chill in the fridge until the cookies are completely chilled. Once chilled, you can either store them for later in the freezer, or bake them right away. See recipe notes for freezing directions.
Preheat oven 350°F. Line a half sheet pan (or cookie sheet) with parchment paper.
Place the chilled cookies on the prepared sheet pan with about 1 - 1.5 inches of space between each cookie.
Bake for 10 - 15 minutes, until the cookies are just very lightly colored on top and along the edges. This takes about 11 - 12 minutes for me.
Remove from the oven and allow the cookies to cool for a few minutes and then transfer them onto a cookie rack to cool completely.
Repeat with the rest of the cookies with a lined half sheet pan which is either at room temperature or chilled (don't place chilled cookies on a warm pan as this will cause them to start melting and spread too much when baked).
Store baked and cooled cookies in an air-tight container (or ziploc bag) until you’re ready to frost them.