Make batter: Preheat oven to 350 degrees F. Using a small brush, lightly coat three 2 1/2-inch 6-cup muffin pans with melted butter. Dust with flour, tap out excess, and set aside. Place 2 cups flour, 1 1/4 cups milk, sugar, brown sugar, cocoa, 3/4 cup butter, sour cream, eggs, 2 teaspoons vanilla, baking powder, baking soda, and salt in a large bowl. Beat using a mixer set on low speed until combined. Increase mixer speed to medium and continue to beat 3 more minutes.
Bake cakes: Divide batter equally between prepared pans and bake on middle rack of oven until cake tops spring back when lightly touched, 20 to 25 minutes. Cool in muffin pans on a wire rack 5 minutes. Use a knife to loosen cakes from pan sides. Invert cakes onto wire rack and cool completely.
Make cream filling: Whisk remaining milk and flour together in a medium saucepan until smooth. Place saucepan over medium heat and cook, stirring constantly, until thick, about 5 minutes. Remove from heat, cool to room temperature, and set aside. Using an electric mixer set on high speed, beat remaining butter and confectioners' sugar together in a medium bowl until light. Add remaining vanilla, reduce mixer speed to medium, and slowly add cooled milk mixture. Beat 1 more minute.
Fill cakes: Fill a pastry bag fitted with a long, narrow tip (we used a Bismark tube #230) with cream filling. Insert tip into bottom of cake and fill by gently moving tip from side to side while squeezing pastry bag, until cake begins to swell. Gently remove tip and return cake to wire rack. Fill remaining cakes and set wire rack over a baking pan.
Glaze cakes: In a double boiler set over simmering water, melt bittersweet chocolate and shortening together. Once melted, remove pan from heat and let sit 3 minutes. Pour about 1 tablespoon chocolate mixture on top of a cake. Use a small spatula to glaze top and smooth around sides until completely coated in a thin layer of chocolate. Repeat with remaining cakes. Freeze 3 minutes, remove, and let sit until chocolate has set, about 1 hour. Decorate cake tops with remaining cream filling, if desired.