Connecting a brushless motor with hall sensors and position encoder to arduino

Good question - I don't think I found such a shield when I looked a while back,
But you need 3-phase bridge which can sometimes be built from a dual H-bridge
if you have full independent control of all the switches.

I've built 3-phase motor drivers with chips like the FAN7388 driving 6 MOSFETs,
and it tends to use a lot of pins - 3 for halls, 6 outputs to the bridge, 1 analog to read
current...

You can use the hall sensors as a very crude encoder and program a BLDC as a servo, BTW