In theory, fly-fishing is a simple sport: Pick a body of water, choose a fly-fishing rod, select your “fly” (or bait), tie a secure knot, cast your line and, hopefully, land a fish on the other end.

Manchester, VT, is something of a time capsule. It’s a two-stoplight town lined with marble sidewalks, manicured lawns, and immaculately restored colonial homes, many of which date back as far as the ...