In a bowl, with a mixer on high speed, beat butter, brown sugar, and granulated sugar until smooth. Beat in egg yolks and vanilla until well blended, scraping sides of bowl as needed.
In a small 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 to coat in turbinado sugar. Place 1 inch apart on buttered 12- by 15-inch baking sheets. Press your thumb into the center of each cookie to make a 1/2-inch-deep imprint.
Bake cookies in a 325° regular or convection oven until lightly browned, 10 to 12 minutes. If baking more than one sheet at a time in one oven, switch 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 1/2 tablespoon chocolate ganache. Let cool 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 (but not touching) barely simmering water in a pan, 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.
Nutritional analysis per cookie.