Using a stand mixer (or a hand mixer + large bowl) beat chilled & diced butter on low until smooth. Gradually add powdered sugar, 1 cup at a time, blending inbetween. Increase speed to medium-high and mix until sugar and butter are thoroughly combined. Consistency should be like grated parmesan cheese.
Tip: If powdered sugar shoots out of bowl while mixing, drape and loosely hold a paper towel over the exposed area of the bowl.
Add milk and pepperment oil, then beat until smooth. Consistency should now be like thick frosting, but not too sticky.
If adding food coloring, divide the buttermint dough into as many bowls as colors you plan to use. Add food coloring (typically just 1-2 drops is sufficient) and knead it in with your hands. As you work through the next steps, cover any exposed dough with plastic wrap to keep it from drying out too fast.
Prepare a flat surface by dusting it with powdered sugar, then dust your hands with more powdered sugar. Scoop out a golfball sized piece of buttermint dough and roll into a log, roughly a 1/2 inch in diameter, on the sugar dusted surface. Add additional powdered sugar as necessary to lessen any stickiness.
Using a pizza cutter or sharp knife, begin cutting pieces off the dough log that are roughly 1/2 inch in length.
When candy has been cut, set in a single layer on a flat surface (such as a plate or baking sheet). Tip: To help increase drying time, place the candy on a couple layers of paper towels.
When candies have all been cut, dust the tops with more sugar (optional). Allow candies to dry at room temperature, uncovered, for 8-12 hours. Once candies are firm, store in an airtight container, layered with wax or parchment paper, for up to 2 weeks.