Preheat the oven to 375°.
Lightly grease (or line with parchment) two baking sheets.
In a large bowl, combine the sugars, butter, shortening, salt, vanilla and almond extracts, vinegar and baking soda.
Beat until smooth and creamy.
Beat in the egg, beating until smooth.
Scrape bottom and sides of bowl with a spatula to make sure all is thoroughly combined.
Mix in the flour, then the chocolate chips.
Drop by rounded teaspoonfuls onto prepared baking sheets, leaving 1" between them on all sides, they'll spread.
Bake cookies for 7 minutes or more, til' edges are chestnut brown and tops are light golden brown.
Remove from oven and cool on a baking rack. (Chill in refrigerator if you're in a hurry.)
Repeat with remaining dough.
Spoon softened coffee ice cream onto a cookie, then press down with a small drinking glass to flatten.
Top with another chocolate chip cookie.
With spatula or butter knife, scrape off extra ice cream around edges.
Place in freezer and freeze ice cream sandwich until hard.
Roll edges in mini chocolate chips.
Repeat with remaining cookies.
Serve immediately or wrap tightly in foil and freeze.