Beat butter with sugar and oil in a bowl for about 1 minute.
Add egg, vanilla, and coffee and mix until well integrated.
Sift the cocoa powder over this mixture and mix.
Add sifted flour, baking soda, and salt in 2 parts. Integrate well but don't overbeat at this point; only mix to incorporate because the cakes will be tough if beaten too much. If using an electric hand mixer mix at low speed.
Cover the bowl and refrigerate for about 2 hours, until firm enough to scoop.
Preheat oven to 350°F (180°C).
Line a cookie sheet with parchment paper.
Scoop portions of chocolate dough and place with an inch or two of separation between them. I use a small or medium cookie scoop at the most as they grow quite a bit during baking.
Bake for 12 to 15 minutes, until crackled, dry, and still slightly soft when barely pressed.
Let cool completely on a wire rack and fill.
Keep at room temperature for a day or two if you want, or put in airtight containers. You can also store the whoopies without filling for a few days and fill when ready to eat.
Mix butter and cheese until creamy and smooth.
Add 1 cup of powdered sugar little by little until it is very thick. Add more sugar if you want a thicker mixture. You might not need to use the whole 1 1/2 cups.
Place a teaspoon or two of filling on the flat side of half of the cookies. Spread lightly without reaching the edges.
Top with the second cookie and press lightly to the filling spreads and fills the whole cookie.