Sift flour, cocoa, and salt into a bowl; set aside. Melt chocolate in a heatproof bowl set over a pan of simmering water, stirring until smooth; set aside to cool.
Put butter and 1/4 cup granulated sugar into the bowl of a mixer fitted with the paddle attachment; mix on medium speed until pale and fluffy. Mix in yolk, vanilla, and chocolate. Reduce speed to low. Mix in flour mixture until just combined. Refrigerate, covered, 1 hour.
Preheat oven to 350 degrees. Put 6 teaspoons granulated sugar into a small bowl. Form dough into 3/4-inch balls; roll in sugar to coat. Space 1 inch apart on baking sheets lined with parchment. Press center of each ball with your thumb. Bake 10 minutes. Press centers again with end of a wooden spoon, making 3/4-inch indentations. Bake until slightly cracked and set, about 5 minutes more. Cool completely on racks. Unfilled cookies can be stored in airtight containers up to 3 days.
Stir cream cheese and confectioners' sugar in a small bowl. Toss berries with remaining 1/2 teaspoon granulated sugar in another bowl. Spoon cream cheese mixture into center of cookies; top with sugared berries, dividing evenly.