B757 Captain reported receiving a flap asymmetry caution when selecting flaps 1 while configuring for an approach. The flight crew received vectors to reenter the approach and performed a safe landing at destination airport.

Narrative

Abeam ZZZ airport. I called for flaps 1; around 215 knots. We then received an amber caution (TE FLAP ASYM). I divided the cockpit duties; and the First Officer (FO) ran the QRH; while I flew with auto throttles INOP; and worked the radios. We did a long downwind pattern. ATC turned us inbound about 20 miles out. We tracked inbound to about a 10 mile final; and the turned outbound for another small downwind; base and final; in order to finalize everything. We had 1.4 hours of fuel; and requested priority handling. We landed with less then flaps 1; with slats extended; with a Vref of flaps 30 +40. The FO did a marvelous job of running the QRH; communicating well; and with good pacing. I had to focus more on flying the airplane - due to the ATS (Autothrottles) being INOP. After the FO had finished the QRH - to the deferred items - I transferred the plane and radios to him; so I could read the QRH and close the comm loop; and increase my situational awareness. We were landing at a high altitude airport; with a Vref that was flaps 5 maneuvering speed. We were landing with less then flaps 1; but QRH doesn't address moving the alternate flap switch to 20 degrees - to have your slats at full extension. I brought this up to my First Officer; as it wasn't sitting right with me. I thought we would be directed to move the alternate flap switch to 20 degrees; similar to the other flap malfunctions. The FO leaned toward just leaving it at flaps 1. We talked it through. We knew that the flap lever was locked out with the asymmetry; and that we had only selected the L.E. alternate flap switch. So only the slats would be energized to move. Also there was a chance that we were expected to move the slats to full extension (though the QRH didn't specifically mention it) - with this confusion; we both agreed that it was safer to try to fully extend the slats; while knowing that the flaps were de-energized and stuck. We leaned on the side of caution; and agreed that this was the safer course of action. We knew we were landing at a high altitude airport; high deck angle; and a low Vapp speed. We briefed the differences in landing; as well as a possible missed approach. On final our pitch attitude was around 7.5 degrees. The Captain did the landing; in the touchdown zone; with auto-brakes 3. We exited the runway at Taxiway 1. We taxied to the ramp; while monitoring the brake temperatures; and really never saw the temperatures rise. Overall I feel that we communicated well; and handled the situation. The high pitch attitude was a bit unnerving; and we knew the risks of a tail strike. The flare was 1-2 degrees; while keeping power in to assist; in not over flaring.