Gran Canaria's volcanic beaches and year-round spring climate have long made it a favorite winter escape for Europeans, but Americans flying business class from Milwaukee to Gran Canaria still need to think carefully about routing, since no carrier offers anything close to nonstop service on this pairing. The practical answer: connect through Madrid via Iberia, through London via British Airways, or through Frankfurt or Munich via Lufthansa, then take a short intra-European hop down to Las Palmas (LPA). Total journey time typically runs 13-16 hours including the connection, though the transatlantic leg itself is roughly 8 hours. Of the three, I favor the Iberia routing through Madrid-Barajas, since Iberia's A330 and A350 business class cabins offer proper flat-bed seats with direct aisle access on the A350, and MAD's T4 satellite building makes for one of the smoother connection experiences in Europe if you've got at least 90 minutes.
British Airways routes MKE-bound travelers through London Heathrow, and while their Club Suite (found on the 777 and A350 fleet) is genuinely one of the better door-equipped business products flying today, the LHR connection can be brutal during peak summer months due to congestion at T5 — I'd avoid anything under two hours there. Lufthansa's Frankfurt or Munich connections work well if you're loyal to Star Alliance, and their newer Allegris business seats, where deployed, bring a noticeably more private, suite-like feel than their older long-haul product, though Allegris hasn't yet reached every aircraft on this corridor, so it's worth checking your specific equipment before booking. One tip I've picked up from repeat trips: flying into LPA on Saturdays often means better connection availability, since Canarian charter and leisure traffic clusters midweek, leaving weekend business-class award space noticeably more open on the European carriers.
Shoulder season — April, May, September, and October — consistently offers the best combination of fare value and pleasant Gran Canaria weather, avoiding both the winter crowds of British and German sun-seekers and Europe's peak summer fares. Given how much these premium fares fluctuate month to month on a routing this indirect, setting up automated fare alerts is the smartest way to catch a business class fare worth booking before it disappears.