In a bowl, with an electric mixer on high speed, beat butter, granulated sugar, and brown sugar until smooth. Beat in egg yolks and vanilla until well blended, scraping sides of bowl as needed.
In another bowl, mix flour, baking powder, and salt. With mixer on low speed, beat flour mixture into butter mixture until well blended. Cover bowl with plastic wrap and chill until dough is firm but pliable, about 30 minutes.
Place about 1/3 cup turbinado sugar in a shallow bowl. Shape dough into 1-inch balls and roll in turbinado sugar to coat. Place 1 inch apart on buttered or cooking parchment- lined 12- by 15-inch baking sheets. Press your thumb into the center of each cookie to make a 1/2-inch-deep indentation.
Bake cookies in a 325° oven until lightly browned, 10 to 12 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. Transfer cookies to a rack to cool completely (if indentations have disappeared, make them again while cookies are warm).
Carefully fill each indentation with about 1 teaspoon chocolate ganache. Let stand until ganache is shiny and firm to the touch, about 1 hour (or chill for about 30 minutes).
Chocolate ganache. In a heatproof bowl set over a pan of barely simmering water (bottom of bowl should not touch water), occasionally stir 6 ounces chopped bittersweet or semisweet chocolate, 2 tablespoons whipping cream, 1 tablespoon corn syrup, and 1 tablespoon butter until chocolate is melted and mixture is smooth. Remove from heat and let cool until thick but not firm, about 15 minutes. Makes about 1 1/4 cups.
Notes: Nutritional analysis is per cookie. Turbinado sugar is a golden-brown, large-crystal sugar, sometimes labeled raw sugar or Demerara sugar. It is available at natural-foods stores and some well-stocked supermarkets. If you can’t find it, substitute additional granulated sugar. These cookies are best the day they are filled, but you can make both the cookies and the filling up to 3 days ahead. Store cookies airtight at room temperature; chill ganache airtight. Melt ganache over hot water and cool before using.