Captain reported an engine failure during single engine taxi. The flight crew informed ATC of the issue and requested clearance to return to the gate.

Narrative

During taxi engine one failed. Engine one was started normally with the APU. It was briefed that we would use the APU to start engine number 2 during a safe time to do so. I checked the engine after the First Officer said we had a good engine start. I confirmed we had a good engine start. Shortly there after we were given a wave off. We properly stated that we had a tug; tow bar; and wave off. We cleared the area to the left and right and called for taxi. After receiving taxi clearance we began to taxi and conducted the taxi flow. As we were about to taxi across Runway XXL; engine one fail EICAS message appeared and the fail boxed amber message showed up on EICAS and the engine shutdown. We stopped the airplane before the hold short line and advised ATC that engine 1 failed and we would need to return to the gate. I called Maintenance Control and described what was going on; he asked us to return to the gate. Local operations was told that we would need to return to gate as well. We started engine two and taxied back to the gate where a maintenance write up was complete. There was no abnormal indications both before or after the engine 1 fail. N1 was roughly at 30-35% as we were adding power to cross XXL.