Air Carrier Captain reported two windshear alerts in close proximity in which the escape maneuvers were properly executed. After safely completing the recovery; the flight was vectored for another approach.

Narrative

We were on visual approach to Runway XXL; backed up by the ILS. Continuous moderate turbulence below 6000 ft.; with frontal passage approaching the airfield. +/- 15 knots on final. Passing 800 ft. AGL; we received the Red Windshear Warning light; two-tone siren followed by the aural alert; 'WINDSHEAR; WINDSHEAR; WINDSHEAR.' I performed the escape maneuver; and started to clean up the aircraft after climbing through 1000 ft. Approaching our missed approach altitude of 3000 ft.; we then encountered a decreasing performance windshear; descending uncontrollably to appropriately 2400 ft. with a notable loss of airspeed. Shortly after; we transitioned to a performance increasing windshear; with airspeed rapidly increasing to approximately 270 kts. Once safely recovered and level at 3000 ft.; I reengaged the automation and we were vectored around for another approach. We did not get the stick shaker or overspeed the flaps during the event. ATC was notified. Subsequent landing was uneventful. Dispatch was notified.Although I briefed the go-around procedure; we did not review the Windshear Escape Maneuver. There were Windshear Advisories in effect; and this should have clued me into us having the discussion about windshear and possible escape maneuver.