Step 1

Preheat oven to 350°F. Cook pasta in a large pot of boiling salted water until about halfway cooked (it needs to be very firm at this stage so that it doesn’t overcook when baked). Drain, reserving 1/2 cup pasta cooking liquid, and run under cold water to stop the cooking. Drain well.

Step 2

Lightly crush cherry tomatoes with your hands in a large bowl. Add mozzarella, provolone, cheddar, Parmesan, cream, and reserved ½ cup pasta cooking liquid and mix to combine. Season generously with salt and pepper. Add cauliflower and cooked pasta and toss to coat. Butter (or lightly coat) a 3-qt. or 13x9x2" baking dish with butter. Scrape in pasta mixture and spread out into an even layer. Cover dish tightly with foil and bake pasta until hot throughout and steaming when foil is lifted, 20–25 minutes.

Step 3

Remove foil and increase oven temperature to 425°F. Continue to bake pasta until sauce is bubbling and top is browned and crunchy in spots, 25–30 minutes. Let cool slightly before serving.

Step 4

Pasta can be assembled 2 days ahead. Cover and chill until ready to bake.