Heat oven to 450 degrees F. Coat a large baking pan with nonstick cooking spray.
In a large bowl, add cauliflower, squash, parsnips, carrots and pepper. Toss with olive oil and 1/4 teaspoon each of the salt and pepper. Spread out on the baking pan in a single layer. Bake at 450 degrees F for 30 minutes, stirring halfway.
Meanwhile, place the broth in a medium-size saucepan and stir in the cornstarch. Bring to a boil, lower heat and simmer 1 minute until thickened. Stir in the thyme, oregano and remaining salt and pepper. In a large bowl, gently toss roasted vegetables, bread crumbs and sauce.
Fit one of the piecrusts into a deep-dish 9-inch pie plate. Sprinkle 1 tablespoon of the cheese over the bottom. Spoon in vegetable mixture and sprinkle with remaining 1 tablespoon cheese. Place the second piecrust on top and crimp crusts together. Pierce a few times with a paring knife to vent. Brush lightly with the egg-water mixture.
Bake at 450 degrees F for 15 minutes. Lower heat to 425 degrees F and bake for an additional 30 minutes. Remove from oven and allow to cool slightly before slicing.