Air carrier First Officer reported severe turbulence resulting in an injured flight attendant. The reporter stated they encountered 30 to 45 degrees of uncommanded roll.

Narrative

We were flying the second leg of a ZZZ turn to ZZZ1. On the first flight; we had flown from ZZZ to ZZZ1 and went through the same storm system while encountering light to occasional moderate turbulence. We were filed on a similar path on the second flight. Approximately 30 minutes into the flight; in preparation of going through forecast light to moderate turbulence; we had the Flight Attendants sit down and discontinue service. The passenger seat belt sign also remained illuminated the entire time. There were other aircraft taking the same route; one that we mentioned in the cockpit that was at 35;000 ft. We were flying at 37;000 ft. in northern ZZZ2 when we deviated East of our track to avoid a thunderstorm cell to the West; staying approximately 20-25 miles to the East of the cell. Abeam the thunderstorm; we went back approximately due North to put a second cell East of our track by approximately 15-20 miles. While on the back side of the system; at approximately (XA00); we encountered continuous moderate and pockets of severe turbulence. We did not lose control of the aircraft at any time. Furthermore; the ride was not severely 'choppy' or 'jerky' but did induce severe performance changes so the nature of the turbulence was probably more evident in the flight station than the back of the aircraft.The aircraft's autopilot had a very difficult time keeping up airspeed; losing and gaining about 20 kts. At one point; while max continuous power was applied; the aircraft came to about the yellow airspeed bracket. The First Officer put the start switches in FLIGHT about halfway through the turbulence episode. We also encountered several uncommanded aircraft rolls of about 30 to 45 degrees and during the beginning of the episode; we had a ROLL AUTHORITY alert on the pilot flight display which corrected itself quickly. After about 5-7 minutes of the moderate-severe turbulence; the ride began to get better. At this time; we decided to descend to 35;000 ft. and the ride improved as we went North and descended. During the time of continuous moderate pockets of severe turbulence; we were near the tops of the clouds but not on top of them. We did not fly through any red portion radar returns on the weather radar. When we felt the worst of the turbulence had abated; we checked with the Flight Attendants. They had been seated the whole time and at the time said there were no injuries.After we landed; the D Flight Attendant said they had hurt their back. Next; we talked to air traffic control to report the severe turbulence. We also sent an ACARS message to Dispatch as well as to Maintenance. The rest of the flight went without incident; although after about 15 minutes of a smooth ride light turbulence continued off and on until we landed in ZZZ. After landing; I talked to Dispatch and Maintenance on a conference call. The Dispatcher and I also spoke to the Supervisor and the Chief Pilot briefly. It was during these calls that I found out the D Flight Attendant told us their back was hurt but I was unable to speak to them before they left. I wrote the turbulence encounter in the logbook and fully debriefed a Mechanic who took control of the aircraft after it was shut down.