After dozens of transatlantic crossings from the desert Southwest, I can tell you the truth about business class from Phoenix to Milan: there's no nonstop, and anyone promising one is misinformed. Sky Harbor doesn't have the traffic to support a route that specific, so your itinerary will connect through one of three major hubs depending on carrier — American via Philadelphia or New York-JFK into their Flagship Suite product (a proper Delta One-style suite with closing door on the 777 and A321neo), Delta through JFK or Atlanta aboard the Delta One Suite on their A330-900 or A350, or United via Newark or Chicago in Polaris seating on the 767 or 777. All three deliver lie-flat, direct-aisle-access seats on the long Atlantic leg, which is what matters most for the roughly 10.5-hour flight time once you're airborne.
My preference, having routed through all three gateways repeatedly, is JFK — whether flying American or Delta. JFK's connection windows to Milan Malpensa tend to be more forgiving than Newark's, and Terminal 4's Delta or Terminal 8's American lounges give you a proper reset before the overnight leg. If you're on United, Chicago O'Hare in winter carries real weather risk for European connections, so build in a buffer of at least two hours rather than the minimum connection time — I've seen Polaris passengers sprint gates in December after O'Hare de-icing delays. On arrival into Malpensa, request a wheeled cart or porter assistance if you're checked heavy; the walk from certain gates to passport control is longer than it looks on the app.
Seasonality rewards patience here: January, February, March, October, and November consistently produce the softest business class fares on this corridor, as Milan's fashion-week and Lake Como summer crowds thin out. Given how much these fares swing week to week across three competing carriers and connection points, setting up automated fare alerts is the smartest move you can make before booking.