Transylvania rarely appears on a Midwestern traveler's radar, which is precisely why the routing deserves careful study before you book. There is no nonstop option, so business class from Kansas City to Cluj-Napoca requires a transatlantic connection, and the most reliable itineraries route through Frankfurt or Munich on Lufthansa, through Istanbul on Turkish Airlines, or via Bucharest on TAROM after a European codeshare handoff. My preference over dozens of bookings on this corridor leans toward the Lufthansa routing: the carrier's long-haul aircraft out of Chicago or occasionally via a connection from MCI offer Lufthansa Allegris seating on newer configurations, with proper closing doors on select cabins, while the short intra-European hop to Cluj is handled comfortably in business class on an A320-family jet with European-style seating and blocked middle seats.
Turkish Airlines is the sleeper pick for this route, and I say that as someone who has flown their Istanbul connection specifically for the Cluj leg. Their lounge in Istanbul remains one of the most theatrical in the world, with a live cooking station and putting green that make a long layover feel like a destination in itself, and their widebody business class seating on the transatlantic segment offers proper flat-bed comfort with generous width. The insider tip few Kansas City travelers know: booking the Istanbul connection during shoulder months often unlocks better award availability on the transatlantic segment than the Frankfurt or Munich routings, because Turkish releases more premium inventory further out. Arrive at MCI's single terminal with plenty of buffer time regardless of carrier, since morning departures to European hubs cluster tightly and security lines swell seasonally.
January, February, March, October, and November consistently offer the softest fares and best award space on this itinerary, as Romanian tourism demand dips outside summer festival season and Christmas markets. Given the complexity of routing through three possible hub cities, I'd strongly recommend setting fare and award alerts rather than manually checking, since availability on this niche corridor shifts quickly and rarely announces itself.