There's no nonstop path linking the Wasatch Front to the Vistula, which means booking business class from Salt Lake City to Warsaw always involves a connection through one of the big three US carriers' European gateways—Delta via Amsterdam or Paris, United via Chicago or Newark to Frankfurt or Munich, or American via London Heathrow, Chicago or Philadelphia. In practice, Delta's routing through Amsterdam tends to be the smoothest, pairing Delta One's suite with a closed door on select 767 and A330 aircraft out of JFK or Minneapolis, then a short LOT Polish Airlines or KLM hop into Warsaw Chopin. United passengers should angle for Polaris seating on the 777-200 or 787-9 through Newark, since Chicago's O'Hare connections to Frankfurt occasionally shift to older 767 configurations without the newest Polaris suite. American's most reliable play is routing through Heathrow's Terminal 3 or 5 in a Club Suite-equipped 777, then a British Airways or LOT continuation—though transatlantic legs from Dallas or Chicago sometimes fly older 777-200 cabins with flat-bed seating rather than the reverse-herringbone Flagship Suite, so it's worth checking the specific aircraft before booking.
Having flown this corridor more times than I can count, my strongest insider tip is this: build in at least a two-hour connection window at Amsterdam Schiphol or Frankfurt during winter months, since de-icing delays are common on the Warsaw-bound regional jets even when your transatlantic segment lands on time—arriving passengers who cut it close often lose their upgraded seat assignment for the final leg. Autumn and late winter are consistently the softest periods for premium cabin availability across all three carriers, since Warsaw draws far more leisure traffic in summer while business travelers dominate shoulder season, giving Salt Lake City to Warsaw business class shoppers real leverage on award space and upgrades.
Given how thin premium inventory runs on this route outside those favorable months, setting up fare and award-space alerts well ahead of your travel dates is the smartest way to catch the rare moments when Delta One, United Polaris, or American Flagship Business opens up at a reasonable redemption or fare level.