Add the softened butter and maple syrup to a bowl and use an electric hand mixer or stand mixer to cream them together on high speed until smooth, about 1 to 2 minutes.
Add the egg yolk, vanilla, and salt to the bowl and mix on medium speed until incorporated, about 1 minute.
Add in the flour and mix on low speed until it forms a dough. It may seem crumbly at first, but it will form into a soft dough. Do not overmix. It will be slightly sticky but will firm up once it chills.
Scoop the dough into a small bowl and cover it tightly. Place the bowl in the fridge to allow the dough to chill for at least 1 hour or overnight. This step is important and it will allow the flour time to hydrate and make it easier to roll out.
After at least an hour, place the chilled dough on the counter to allow it to slightly soften as you preheat the oven to 350 degrees F (180 degrees C).
Sprinkle 1 to 2 tablespoons of flour on a sheet of parchment paper and place the dough on top. Flour a rolling pin and roll the dough out until it is about 1/4 of an inch thick for crunchy cookies. If you prefer softer cookies, roll it out slightly thicker.
Use cookie cutter shapes to cut out the dough directly on the sheet of parchment paper. Peel away the scraps and reroll them out to cut out more shapes from the dough until all of the dough is used. Add additional flour as needed to prevent the dough from sticking. Transfer the parchment paper directly to the baking sheet. Doing this helps prevent the shapes from becoming distorted from transferring them.
Bake the cookies for 8 to 10 minutes until the edges are lightly golden brown. Allow the cookies to cool completely before decorating them.
To make homemade cookie icing, mix powdered sugar and milk with a fork until smooth, adding a little more liquid as needed until you reach the desired consistency. Frost the cookies and add sprinkles immediately, before the icing hardens and sets.