Preheat your oven to 375 degrees F and line a baking sheet or two with parchment paper.
In a large bowl, add the two sticks of butter (stick in the microwave to soften a bit if necessary) and the sugar (1 cup). Cream together with a hand or standing mixer on high speed for about 3 minutes.
Add the egg, baking powder (1 teaspoon), and salt (¼ teaspoon) and mix for another minute.
Add the flour (2 cups) and mix until just combined. Add the crushed peppermint (½ cup) and mix again until just combined.
In a shallow bowl, stir together ½ cup crushed peppermint and ¼ cup sugar.
Using a small cookie scoop, measure out the dough and scoop directly into the bowl of peppermint and sugar. Using your hands or the bottom of a glass, press gently on top of the dough to coat well with the peppermint and sugar. Don't press too hard; you want them to be about a half an inch thick.
Place cookies on the parchment-covered baking sheet. At this point, if the peppermint and sugar didn't stick very well to some of them, you can sprinkle a little extra on top. Bake at 375 degrees F. for about 10 minutes, or until jut starting to get golden around the edges. In the meantime, you can prepare a second batch for the oven on another baking sheet.
Optional: These cookies flatten out quite a bit when baking. If you want a thicker circle cookie: Immediately after you take them out of the oven while they are still hot, use a wide glass or circle cookie cutter to run around each cookie gently to shape them into a circle.
Transfer cookies to a cooling rack to cool for a few minutes and enjoy!