Place cauliflower florets in a large saucepan. Add the chicken broth and bring to a boil. Cover and simmer until very tender, about 12 minutes. Drain thoroughly and return to the pot over low heat. Cook about 2 more minutes to dry out excess moisture, stirring constantly. It's okay that it breaks apart.
Pour cooked cauliflower into food processor fitted with the metal blade. Add butter, cream cheese, sour cream, HALF of the cheddar cheese, salt, pepper, and eggs. Pulse to combine. Fold in the green onions by hand.
Spray an oven-proof casserole with vegetable oil. Pour cauliflower mixture into casserole dish and sprinkle evenly with remaining 1/2 cup cheddar cheese and all of the parmesan cheese. Sprinkle with the smoked paprika. Bake in a preheated 375°F oven for about 45 minutes.