Challenger 300 Captain reported loss of power and oil pressure in one engine. Pilot shut down the engine and returned to departure airport.

Narrative

We departed ZZZ on the SID. ZZZ Departure vectored us off route for ATC reasons. We were then handed to ZZZ Center at that time. We were approximately 12;000 ft. ZZZ Center instructed us to climb to 14;000 feet and go direct ZZZZZ to resume the ZZZZZX departure.Approximately two minutes later; we heard a vibrating grinding noise that shook the airplane about 30 seconds after that we got a master warning on our house and the associated alarm for an engine accident. As the pilot flying; I performed the emergency memory items; thrust level; retard; and the engine began to pull down. We assessed the engine instruments. There was zero N-1 ZERO N-2 and ZERO OIL PSI. We performed the engine shut down procedure [requested priority handling] and returned to ZZZ. We were vector back to the airport where I performed a visual approach single engine to a normal landing taxi to the ramp under our own power.During the initial portion of the failure; the aircraft was very difficult to control as the engine was seized. We were told to descend to 11;000 and I descended below that during the fight to control the aircraft once aircraft was back under control told ATC we could maintain altitude they cleared us down to 10;000. I had instructed my copilot to [request priority handling]. I don't know if he actually did it because ATC came on and said they were gonna do it for us I took over the radio and said negative. I will [request the priority handling] now and I [advised] type of situation; passengers; and fuel on board.