First, make the filling: Line a baking sheet with parchment paper. In a large bowl using an electric hand mixer or in the bowl of a stand mixer with the paddle attachment, beat cream cheese, 1/3 cup granulated sugar, sour cream and 1 teaspoon vanilla until creamy and smooth, about 1 minute. Spoon filling, one tablespoon at a time, onto lined baking sheet (you should end up with 12 scoops/dollops). Freeze dollops 2 hours or until solid.
Meanwhile, make the cookies: In a large bowl, sift or whisk together flour, cocoa powder, baking powder, salt and baking soda. In a separate large bowl, whisk together 1 1/4 cups granulated sugar, melted butter, buttermilk, red food coloring (if using), 1 teaspoon vanilla and eggs until smooth. Use a spatula to fold flour mixture into sugar mixture until just combined. Cover bowl with plastic wrap; refrigerate 30 minutes to firm up (dough will still be soft, but more pliable).
Heat oven to 350°F. Line 2 baking sheets with parchment paper. Place powdered sugar in a shallow bowl; cover hands with extra powdered sugar. Scoop 1 generous tablespoon of cookie dough and flatten into a circle. Place 1 dollop of frozen cream cheese mixture in center, then top with another 1 generous tablespoon of dough. Use powdered sugar-covered hands to enclose dough around dollop and shape into a ball. Roll ball in powdered sugar and place on prepared baking sheet. Repeat with remaining dough and cream cheese dollops, spacing cookies at least 2 inches apart on prepared baking sheets (6 cookies per sheet). Continue to coat hands in powdered sugar as you go to keep dough from sticking.
Place baking sheets in the oven; bake 10 to 15 minutes or until cookies have spread and edges are set, rotating baking sheets halfway through bake time. Cool cookies 10 minutes on baking sheets, then transfer to a cooling rack to cool completely.
Store fully cooled cookies in an airtight container in the refrigerator for up to 4 days.