Preheat oven to 375 degrees. Line baking sheet with parchment paper.
In heavy saucepan over medium heat, melt shortening and butter. Add 3/4 cup flour and stir until well blended. Cook and stir until mixture is a medium dark roux. Remove from heat and pour in bowl. Cool in refrigerator.
In medium bowl, stir together remaining flour, baking powder, baking soda, and salt. In large mixing bowl, beat sugars and roux mixture until light and fluffy. Add eggs and vanilla and beat at low speed until well combined. Add remaining flour mixture beating at low speed just until combined. Stir in chocolate chips.
Drop dough 1 heaping tablespoon one at a time on to prepared baking sheet. Bake for 9 to 10 minutes until edges are lightly browned. Cool on baking sheet for 1 minute. Cool completely on wire racks.