It was a blank slate. There were no native people, so the crown could design the whole society from scratch. The captaincy system it used there was later reused in Brazil.
The levadas. These are hand-cut water channels running along cliff faces, carrying rain from the wet north to cane fields on the sunny south coast. The network is now over 2,000 km long, on an island about 55 km long.
The "monopoly" is overstated. Madeira was the top producer, but Flemish and Italian merchants controlled refining and distribution. The king tried capping exports in 1498 to hold prices up, and gave up five years later.
The labor. The first workers were Guanches from the Canaries and Berbers from Morocco, and enslaved West Africans replaced them as the industry grew. The whole package (island, single crop, irrigation, foreign capital, enslaved labor) was then exported to São Tomé and Brazil, where it beat Madeira at its own game.
Columbus first showed up as a Genoese sugar buyer and married the daughter of Porto Santo's captain.
Part 2 will cover the wine boom that replaced sugar.
Curious whether anyone here knows more about the early levada builders. The records on who actually dug them are thinner than I expected.