A319 pilot reported engine malfunction after takeoff. Returned and landed uneventfully.

Narrative

Sequence of events for Aircraft X ZZZZ-ZZZ on Date 0. All operations were normal up to engine start. The #1 engine had a failed start on first attempt at ZZZ. The start sequence automatically attempted a second start without incident. This was identified as fairly common by the Captain at high pressure altitude airports and did not raise concern. We taxied to Runway XX for departure with strong gusty winds and opted to use ignition on due to wind sheer reported of 10 knot gain on final. The First Officer (FO) was the Pilot Flying (PF) and we noted a louder than normal buzz from the engines on the takeoff roll. There were no associated abnormal engine indications that would have warranted a reject. Shortly after takeoff and after gear up an advisory" white advisory was flashing on the engine display and we noted #1 engine vibration varying from 0-9 while climbing through 7000 feet MSL. We made our turn at 8000 ft. MSL per departure instructions and while still analyzing the engine situation. Captain and FO discussed the situation and agreed the safest decision was to make an emergency return to the airfield. The FO continued flying while the Captain coordinated with ATC; Flight Attendants; and passengers. The Captain [requested priority] and we received short vectors to intercept the ILS for Runway XX. The FO displayed exceptional poise and airmanship as pilot flying and executed a soft overweight landing; at 140;000 lbs; and with challenging winds in the high pressure altitude airport. Fire crew chased the uneventful landing and reported no unusual visuals for the aircraft. We expected to taxi clear and have fire crew [cancel priority handling]; however we were simply given taxi instructions to a hard stand with emergency crew in chase. We taxied to the stand; shut down like normal; and the Captain continued coordination with the Flight Crew; Passengers; and ground personnel until the aircraft was normally deplaned. The Flight Attendants expertly handled safety protocol and confidently executed their duties during all aspects of the emergency and deplaning. After deplaning the Captain; accompanied by the First officer; gave an official statement of the event to Aviation Authorities. Mechanical malfunction."