Preheat oven to 350. Add the shortening, butter, and brown sugar to a stand mixer. Mix for 2 minutes. Add eggs and mix until just combined.
Add flour, cornstarch, baking soda, and salt. Mix until dough just comes together.
If making large, Crumbl style cookies, scoop out 1/2 cup of dough per cookie. You can fit 5-6 cookies on a normal cookie sheet. Roll each cookie into a ball and flatten it slightly with your hand. Using a wooden skewer or chopstick, lightly press 4 lines into each cookie, criss-cross, to give a waffle look.
Bake in the oven for 9-11 minutes, until cookies are just set.
While the cookies are cooling, make the frosting. Add butter to a stand mixer and mix for 2 minutes. Add powdered sugar and vanilla and mix for an additional 2 minutes. Add a tablespoon sized scoop of frosting to the top of each cookie.
Right before serving, drizzle with maple syrup and enjoy!