Burnt-sugar vanilla butter cookies

In a medium bowl, whisk the flour, baking powder, and salt.
In a stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth, about 1 minute.
Add 1½ cups of the sugar and the vanilla seeds or extract and beat on medium speed until well blended, about 2 minutes. Add the eggs and yolks one at a time, mixing until blended after each addition. Add the flour mixture and mix on low speed until just blended, about 1 minute.
Turn the dough out onto a large piece of plastic wrap. Using the plastic as an aid, gently knead into a smooth dough (the dough will be soft). Shape into a 12-inch round log about 3 inches in diameter and wrap in the plastic. Cut an empty paper towel roll open. Gently rest the dough in the roll and refrigerate until chilled and very firm, about 4 hours. (The dough may be refrigerated for up to 3 days or frozen for up to 1 month).
Position a rack in the center of the oven and heat the oven to 350°F. Line 2 or more cookie sheets with parchment or nonstick baking liners. Put the remaining 1/3 cup sugar in a small bowl.
Cut the dough into slices about ¼ inch thick. Gently press one side of each cookie into the sugar to coat completely. Arrange the cookies sugar side up about 1 inch apart on the lined cookie sheets. Save the rest of the sugar for decorating the cookies.
Bake, one sheet at a time, until golden-brown, 11 to 14 minutes. Let the cookies cool on the sheet for about 5 minutes and then transfer them to a rack to cool completely. (The cookies can be stored in an airtight container at room temperature for up to 3 days before proceeding).
Dip the sugared side of the cookies into the remaining sugar. Arrange the cookies sugar side up on a flameproof work surface. Pass the flame of a small kitchen torch over the cookie tops until evenly caramelized. Let cool completely, about 3 minutes, before serving.