Line 2 cookie sheets with parchment paper and set aside.

In a large mixing bowl, add the shortening, butter, cream cheese, orange zest, sugar, eggs, vanilla extract, and orange extract. Mix until light and fluffy.

Whisk together the flour, salt, and baking powder in a medium bowl.

Add the dry ingredients to the wet ingredients and blend until well combined.

Divide the dough into 14 equal-sized balls, each weighing approximately 3.6 ounces.

Place seven balls per cookie sheet on the prepared cookie sheets and refrigerate for 2½ hours.

Preheat the oven to 350°F. Bake for 14 minutes, then gently press the hot cookie to create a flat surface. Continue baking for an additional 4 minutes.

Slide the cookies, still on the parchment paper, onto the counter to cool completely.

Transfer cooled cookies to a wire cooling rack. Dip the cooled cookies in orange glaze.

Add the sugar, orange juice, orange extract, and orange zest in a medium bowl. Whisk until smooth.