Mix oat flour, coconut flour, salt, and baking soda together in a bowl.
Cream 1/2 cup plus 2 tablespoons shortening and coconut sugar in a bowl with an electric mixer until light and fluffy. Add eggs, one at a time, beating well and scraping down the sides of the bowl after each addition. Mix in vanilla. Slowly mix in dry ingredients. Stir in chocolate chips. Place dough in the refrigerator for 30 minutes.
Preheat the oven to 350 degrees F (175 degrees C).
Roll tablespoonfuls of dough into balls. Place on an ungreased cookie sheet and flatten with wet fingers.
Bake in the preheated oven until golden brown, about 14 minutes; cookies will be tender when they come out of the oven. Let rest on the cookie sheet for 10 minutes, then transfer to a wire rack to finish cooling completely.