Pula's tiny Istrian airport doesn't accept widebody long-haul jets, which is precisely why the route from Minnesota demands a smart connection rather than a search for something nonexistent: a nonstop. There is no direct service, so business class from Minneapolis to Pula requires routing through a major European or Turkish hub, with the actual long-haul business product experienced on the transatlantic leg before a short regional hop finishes the journey. Lufthansa via Frankfurt or Munich remains my preferred option for the transatlantic segment, especially now that Allegris is gradually rolling out on select 787 and A350 routes from the US, though travelers should confirm aircraft type at booking since Allegris isn't yet fleet-wide. Turkish Airlines via Istanbul is the other compelling choice, and I've found their lie-flat business seat and famously generous catering make the long haul from MSP genuinely enjoyable, especially paired with a stopover in the excellent Istanbul Airport lounge.
Once you've crossed the Atlantic, the connection onward to Pula is typically operated by Croatia Airlines (OU) on an Airbus A319 or Dash 8, strictly economy configuration — a reminder that the luxury of this journey lives entirely in the long-haul segment, not the finish line. My insider tip: book the Munich-to-Pula seasonal Lufthansa Group connection when available in peak summer, as it shaves hours off itineraries that otherwise route through Zagreb or Frankfurt with tighter connections. Arrive into Munich or Frankfurt with at least 90 minutes of buffer if connecting onto Croatia Airlines, since their check-in counters close earlier than most US travelers expect, and Istanbul's sheer terminal size means Turkish transfers deserve similar caution despite the airline's efficient transfer desks.
Seasonality matters enormously here — Istria is a summer destination, but airfare logic runs opposite to tourist demand. April, May, September, and October consistently offer the strongest business class value, as airlines discount before and after the July-August crush when leisure travelers flood both the transatlantic and intra-European legs. Given how much these fares fluctuate with capacity on the connecting regional flights, I'd strongly recommend setting up automated fare alerts to catch the inevitable dips rather than checking manually.