Preheat oven to 350°F. Line a baking sheet with parchment paper.
In a small bowl, whisk together flour, baking soda, and salt. Set aside.
In a large mixing bowl, cream together butter and granulated sugar with an electric mixer until light and fluffy, about 2-3 minutes.
Beat in egg, vanilla extract, and peppermint extract until well combined.
Gradually add the flour mixture to the wet ingredients and mix until just combined. Scrape down the sides of the bowl as needed.
Fold in the 3/4 cup (about 4.5 ounces) of the white chocolate chips or chopped bars and 1/3 cup of the crushed peppermint candies. Mix until evenly distributed throughout the dough.
Drop rounded 2 tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart. Refrigerate the dough for 15-30 minutes.
Bake 10-12 minutes or until the edges are lightly golden. The centers may look slightly underbaked, but they will firm up as they cool. If desired, while the cookies are warm, shape into perfect cookie circles with a large round biscuit cutter by circling the cookie dough 3-4 times. Cool on the baking sheet for about 5 minutes before transferring to a wax paper or parchment paper lined wire rack or countertop to cool completely.
Melt the remaining white chocolate in a small bowl. Drizzle on top of the cooled cookies and sprinkle on the remaining crushed peppermint.