In a large mixing bowl, beat butter with an electric mixer for 30 seconds. Add granulated sugar, salt, and baking soda; beat until combined. Beat in egg and the 1 teaspoon vanilla. Beat in cocoa powder and as much flour as you can with the mixer. Stir in any remaining flour. Shape into a 2-inch log (about 10 inches long). Wrap in parchment or waxed paper and chill at least 2 hours or up to 24 hours.
Preheat oven to 375 degrees F. Slice dough into 1/8-inch rounds. Place on ungreased cookie sheets. If desired, poke several times with a fork. Bake in preheated oven for 8 to 10 minutes or until edges are firm. Remove and cool on wire racks.
For filling, in another large mixing bowl beat the 3 tablespoons butter and cream cheese with the mixer on medium speed until combined. Gradually beat in the powdered sugar, 1/2 teaspoon vanilla, and the 1/4 teaspoon salt. Beat in enough half-and-half to make of spreading consistency. Spread about 1 tablespoon filling on bottom of one cookie; top with second cookie, bottom side down. Repeat with remaining cookies and filling. Cover and chill until firm. Makes about 24 cookie sandwiches.