You can substitute semisweet chocolate chunks or chips for the milk chocolate.
Heat oven to 375 degrees. Line two baking sheets with parchment, and set aside. In a medium bowl, whisk together the flour, baking soda, and salt; set aside.
In the bowl of an electric mixer, combine the butter and vanilla; beat until fluffy. Add both sugars, and beat until light. Add the egg, and beat until combined. Add the reserved dry ingredients; beat on low speed just until combined. Stir in the chocolate chunks. Form dough into a ball, and cover with plastic wrap; refrigerate until firm, at least 2 hours or overnight.
Remove dough from refrigerator. Using an ice-cream scoop, shape dough into 2-inch-diameter balls. Place balls on prepared baking sheets, spaced 4 inches apart. Flatten each ball into a 3-inch-diameter disk. Chill until firm.
Transfer to oven, and bake until edges are golden but centers are still soft, 15 to 17 minutes. Remove from oven, and transfer to a wire rack to cool completely. Store in an airtight container up to 2 days.