Air Carrier Captain reported inflight engine shutdown due to fuel system malfunction during climb and return to departure airport.

Narrative

Took off out of ZZZ on Runway XXL. Starting fuel was 19;000 lbs had 2;000 in the center tanks at push. Flew the ZZZZZ departure to ZZZZZ1 transition. We were given direct to ZZZZZ2. Climbing through about 18;000ft I noticed the imbal notification under the left fuel tank indicator. I alerted the FO and we watched the fuel quantity and it was dropping 100lbs about every 15-20 seconds. At that point we asked ZZZ for a level off at 20;000ft while we ran the checklists. The imbalance was 1;100lbs at this point. I asked the flight attendants to look out at the left wing and engine for any indications of fuel leaking. They reported back that they didn't see anything. We ran the NG fuel leak checklist. At step 6 it says to note the fuel and start a timer. Within about 2 mins we were down more than the 500lbs the checklist calls for. At that point we [requested priority handling] and completed the checklist which called for an engine shutdown. We proceeded back to ZZZ and performed a single engine ILS approach to RWY XYR. Landed uneventfully and taxied to the Gate XX.