I do very little residential work. Using a 2P breaker is considered 208V single-phase, not 240V. 240V sounds weird to me.
The only way that I'm aware of in order to get 208 single phase is with a 208 y/120 3ph4w supply. With this system you can feed a 208 1ph2w load from the line to line. To do this you would install a 2p breaker in a 208y/120 3ph4w panel. .for 120v 1ph2w from a line to neutral you instal a 1p breaker which would proved 120 between that line and the neutral.