Simmer cream, uncovered, for 5 to 10 minutes until reduced to 1/2 c. Cool 10 to 15 minutes under refrigeration; reserve. Blend barbecue sauce into cream. Brush each pizza crust with 1 T. oil; top each with 1/2 c. reserved sauce. Roast peppers, seed, peel; slice in 1/2" slices. Season squash with olive oil, salt and pepper; grill.
Season eggplant lightly with salt and allow to sit for 20 minutes to sweat off bitter juices. Rinse and dry; grill. Arrange all roasted and grilled vegetables equally over sauce on each pizza. Sprinkle cheese equally over vegetables.
Cover cheese with 6 to 8 tomato slices. Bake in preheated conventional oven at 450 F for 8 to 10 minutes or until crust is cooked and cheese bubbles.