What is the best way to disconnect a frozen/rusted-on shut off valve? Both the hot and cold pipes coming in under the bathroom sink are rusted to the shut off valves and the valves themselves cannot be shut off.

Galvanized or copper pipes coming to the valves? Ig you have old galvanized pipes its best to cut off the pipe and then unthread back to a fitting where you could transition to something like PVC, CPVC, PEX or copper.

These valves. Are they compression of threaded valves? Have you shut the water off to the house and backed the bonnet packing nut off to see if you can remove the stem? All your valves might need is a good lube job. Regards Tom

I am 99% sure they are galvanized pipes with a threaded connection. We did shut the water off to the house to check out the situation. I don't know what the bonnet packing nut is though. :(

I don't know what the bonnet packing nut is
A bonnet packing nut is the nut on the stem of the valve. T thought that if you could get the valve open and the stem out you could clean up the valve, lube the threads on the stem and reassemble using the same valves. This would save you time and hassle. If you can't do that then remove the supplies back to the valve and simply replace the threaded angle stops. Good luck. Tom