Combine tomato and water; let stand 15 minutes. Drain and cut into thin slices.
Separate breadstick dough into strips. Coil 1 strip of dough. Add second strip to end of first, pinching ends together; continue coiling. Repeat procedure with remaining strips to make an 8-inch-round coil. Press coiled dough into a 13-inch circle, and place in a 9-inch pieplate coated with cooking spray. Fold edges under, and flute; sprinkle with cornmeal.
Drain artichokes in a wire-mesh strainer, reserving liquid; chop artichokes. Pour liquid into a nonstick skillet; place over medium-high heat until hot. Add garlic and onions; saute 5 minutes. Stir in basil and oregano; remove from heat.
Arrange tomato, artichokes, and onion mixture over dough; sprinkle with cheeses.
Combine milk and remaining 3 ingredients in container of an electric blender; cover and process until smooth. Pour over cheese. Bake at 375° for 35 minutes. Let stand 10 minutes.