A Center Controller reported a departing air ambulance flight on initial climb turned back to the departure airport flying below the minimum IFR altitude and in conflict with an arriving air carrier.

Narrative

I was working [Sector] X and Y combined ground up due to low staffing. Aircraft X was inbound to ZZZ on a visual approach. There was a VFR aircraft climbing south of the airport. I called the traffic. The traffic called up as Aircraft Y requesting IFR. I issued a squawk and told him to maintain VFR as I had an aircraft on a visual. Aircraft Y was southeast of the airport when I thought I heard him say he would stay clear of the arrival path. I was distracted by ZZZ1 arrivals in sector X. I cleared Aircraft Y to his destination; I believe I gave him the clearance leaving [Flight Level] 100. He did not read it back and I asked if he received it. He then stated that he was returning to ZZZ due to an issue. I did not understand what he said the issue was. I canceled Aircraft X's clearance and told them to maintain 080. I think I then issued a heading. By this time Aircraft Y was below the MIA but because I had already issued a clearance I felt like I had to give him an IFR clearance to ZZZ. I cleared him direct and asked if he had the field in sight. When he affirmed I cleared him to a visual. In the confusion I forgot to verify weather or notams. Aircraft Y canceled IFR and I gave Aircraft X the visual but by then they had to maneuver to descend. Suggestion: Verify the request of an aircraft before issuing IFR clearance. Increase staffing so that sectors aren't combined during an arrival rush