Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.
In a standing mixer fitted with a paddle attachment or with a handheld mixer, cream together the shortening, butter and sugar until light and fluffy. Beat in the vanilla and eggs. Add the flour, soda and salt and mix to incorporate completely. Stir in the dark and white chocolate by hand.
Using two soup spoons, drop 6 large rounds of the dough onto each lined baking sheet. Bake for approximately 10 minutes or until the edges of the cookies are a dark golden color, but the centers are still light. Let cool for a few minutes on the cookie sheets and then transfer onto a wire rack. Repeat this process with the remaining dough. Store in an airtight container to keep the crispy goodness!