Preheat oven to 350. In small measuring cup, mix together heavy whipping cream and instant espresso powder. In a large bowl, with an electric mixer on medium speed, cream 1 cup butter and 2 cups sugar until light and fluffy, about 6 minutes. On low speed, add eggs one at a time, until well combined. Add cream/espresso mixture and vanilla. In medium bowl, whisk together flour, baking powder, baking soda, and salt until combined. Add cocoa and stir in oats. Gradually add to creamed mixture in thirds and mix well. Drop by tablespoonfuls onto parchment paper lined baking sheets. Bake for 10 minutes or until set. Allow to cool on cookie sheets for 5 minutes before transfering to wire racks to cool completely.
Meanwhile, in a saucepan, combine the cornstarch, 4 TBS. cocoa, and water until smooth. Stir in 1 c. sugar and 4 TBS. butter. Bring to a boil over medium heat, stirring constantly; cook and stir for 2 minutes or until thickened. Remove from heat; stir in vanilla and 1/2 tsp. instant espresso powder. Cool completely, stirring occasionally, before spreading on bottom half of cookies and topping with remaining cookies.