Preheat oven to 500 degrees F. Line a large baking sheet with foil. Sprinkle foil with cornmeal; set aside. In a medium bowl combine flour, salt, baking powder, and pepper. Using a pasty blender, cut shortening into flour mixture until the mixture resembles coarse crumbs. Make a well in the center of the mixture. Add water and stir with a fork until combined. Knead dough a few times until smooth.
Divide dough in half. On a lightly floured surface, roll each dough portion into a 14x5-inch oval. Arrange dough ovals on the prepared baking sheet. Brush with 1 tablespoon of the oil. Bake for 11 to 13 minutes or until lightly golden brown.
Meanwhile, for topping, in a large skillet heat the remaining 2 tablespoons oil over medium-high heat. Add mushrooms and onion to hot oil; cook and stir for 3 minutes. Add asparagus; cook and stir about 3 minutes more or just until tender. Remove from heat. Stir in chicken, parsley, mustard, and thyme.
Spoon half of the topping over each crust. Sprinkle with cheese. Bake about 5 minutes more or until cheese is melted.