gary p wrote:
The easy-button is a Wolf Tooth Road Link and any late model Ultegra or 105 long cage derailleur. You can easily run a 40T rear cog.....as long as you're conscious to never go big-big.
Off-the-wall suggestion, that's wide range and very inexpensive, is the
Microshift Advent Group. It's rated for an 11-42 rear cassette and 47t overall, meaning it will work in a 2x configuration with up to 16T differential between big and small ring. Only 9 cogs, though. And it looks like you have to go off-series for the left brifter.
I'm using the long cage microshift clutch 10 speed along with their matching bar end shifter on my cross bike with a pretty big rear cluster (36 or something) on one wheel. It works well for reducing chain slap, it shifts a little like a dump truck but i'm using it in friction mode so I can throw in 8 or 9 speed wheels and use up my older equipment. The RD is quite heavy, if you care about that.
The wolftooth is an elegant solution, we use it on some of the junior bikes and it allows for big cogs without having to buy new equipment