Air carrier Captain reported a severe jolt of turbulence during cruise which resulted in a Mach limit exceedance and an altitude excursion.The Captain executed the upset recovery with no injuries or damage.

Narrative

Initial briefing with (Flight Attendants) FAs; I indicated the area and approximate time of weather on route. It was also stated to the passengers during my boarding announcement. Approaching area of weather; my First Officer (FO) turned on the seat belt sign and made a PA. I notified the FAs via interphone of upcoming weather and to plan to take their jump seats. A few minutes later I made a 'Take your jumpseats' PA; followed by another PA to the passengers to make sure their seat belts were securely fastened. I called the FAs again to verify everyone was seated and to tell them approximately how long to be seated. ATC had already reported a PIREP in our area of moderate turbulence and we were already deviating around the storm in coordination with Dispatch and following other aircraft.Within about 1 second; we exceeded Mach limit; got the clacker; and encountered a severe jolt of turbulence. The turbulence continued for several seconds while I recovered. I followed the upset recovery procedure but failed to verbalize the steps aloud. I also retarded the thrust levers; but realizing my potential error; I stood them back up and fully deployed the speed brakes instead. According to the jump-seater; we gained about 400 feet and reached about 300 kts; or an estimated M.84. The event and its recovery took roughly 5-10 seconds. We notified ATC and Dispatch and checked in with the FAs. No reports of injury or damage in the cabin; and the only fatality was a spilt pot of coffee.