Cook the twisted pasta in heavily salted boiling water until 2 minutes short of al dente. Add the broccoli for the final 2 minutes. Reserve ½ cup pasta water, drain both, and set aside.

Pat the steak pieces completely dry — moisture is what stops the crust from forming. Season with ¾ teaspoon salt, ¾ teaspoon cracked black pepper, the garlic powder, and smoked paprika.

Heat the olive oil in a large heavy skillet over high heat until just smoking. Sear the steak in two batches, 2 minutes without moving for a dark crust, then flip and sear 90 seconds more, leaving the centers pink.

Reduce heat to medium. Return all the steak with 3 tablespoons butter and 4 cloves of the garlic. Toss 45 seconds, spooning the sizzling butter over, then transfer to a plate with all the juices.

In the same skillet, melt 2 tablespoons butter over medium heat. Add the shallot and cook 3 minutes, then add 3 cloves of the garlic and cook 1 minute, scraping up the browned bits.

Whisk in the flour and cook 1 minute. Pour in the beef broth while whisking to deglaze fully.

Add the heavy cream and milk. Simmer 4 minutes until thickened.

Reduce heat to low. Whisk in the cream cheese until melted, then add 1¼ cups of the Parmesan, 1 cup of the mozzarella, and the provolone in handfuls, stirring until pale gold and smooth.

Season with Italian seasoning, onion powder, red pepper flakes, remaining salt, and remaining black pepper.

Stir in the remaining 2 tablespoons butter and the last 2 cloves of garlic.

Add the pasta and broccoli and toss until the sauce fills the grooves, loosening with reserved pasta water as needed.

Spoon extra sauce over the top, scatter the remaining ½ cup Parmesan and ½ cup mozzarella over it, then fold the steak and its resting juices among the spirals so both sit together. Finish with parsley.