Preheat oven to 350º. Grease a 13"-by-9" baking dish with butter.
In a large heatproof bowl, combine cauliflower and 1 cup water. Microwave until tender, about 5 minutes. Drain and repeat with broccoli and remaining 1 cup water.
In a large bowl, using a rubber spatula, stir cream cheese and sour cream. Stir in tomatoes, white scallion parts, half of green scallion parts, garlic, cornstarch, ranch powder, red pepper flakes, ½ teaspoon salt, and ¼ teaspoon black pepper.
Add broccoli and cauliflower, folding to combine and coat in sauce (it’s okay if veggies are warm, as this will help loosen sauce).
Fold in 1 ½ cups mozzarella. Pour into baking dish, spreading in an even layer. Sprinkle with Parmesan and remaining ½ cup mozzarella.
Bake casserole 20 minutes. Turn oven to broil and broil on high until cheeses are browned, 4 to 6 minutes. Top with remaining green scallion parts and serve.
