Preheat your oven to 350 degrees F.
Combine the flour and salt in the bowl of a stand mixer fitted with the paddle attachment and paddle on low speed until well mixed.
Add the butter and water and beat on low speed until the mixture starts to come together in small clusters.
Spread the clusters on a parchment lined sheet pan. Bake for 20 to 25 minutes, breaking them up occasionally and keeping an eye on them toward the 20 minute mark. The crumbs should be golden brown and still slightly moist to the touch at that point; they will dry and harden as they cool.
Let the crumbs cool completely before using in a recipe or eating. The crumbs can be stored in an airtight container for 1 week at room temperature or 1 month in the fridge or freezer.
Combine the shortbread crumbs and milk in a blender, turn the speed to medium-high, and puree until smooth and homogenous. It will take 1 to 3 minutes (depending on your blender). If the mixture does not catch on your blender blade, turn off the blender, take a small teaspoon, and scrape down the sides of the canister, remembering to scrape under the blade, then try again.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and powdered sugar. Cream together on medium-high for 2 to 3 minutes, until fluffy and pale yellow. Scrape down the sides of the bowl with a spatula.
On low speed, paddle in the contents of the blender. After 1 minute, increase the speed to medium-high and beat for another 2 minutes. Scrape down the sides of the bowl. If the mixture is not a uniform, very pale, barely tan color, give the bowl another scrape-down and another minute of high-speed paddling.
Use the frosting immediately, or store it in an airtight container in the fridge for up to 1 week.