I watched this vid of a Tesla P100D in the ludicrously named ludicrous (plus?) mode on a dyno. Video included for reference only.
I didn't watch it all - was most interested in the output. See screenshot here

So it's a peak of 920 lbs.ft (blue line - torque is the only thing you feel on your arse-dyno remember) and 589bhp (black line).
Electric motors create their peak torque at 0rpm (so in theory if they had started the dyno run from 0mph it would have been an even higher peak torque figure - but they suffered wheelspin) and torque tails off as motor speed rises. This is clearly visible in the torque trace, and rather interesting as it ends up looking not-dissimilar to a smoothed version of the output of an IC engine with gears.
The EV dyno trace is from "slow" mph to VMax, which you don't usually see in a dyno trace. Usually you'd use 4th on a dyno (or whichever gear in the gearbox is closest to 1:1 to minimise losses), so the dyno trace will be measured from "moderate" mph to whatever the VMax is in that specific gear. If you ran the dyno over the full speed range of the car, using the gears, then you'd see something like this. Yes I did just draw this in powerpoint and then take a photo of my screen with my phone.


Hence the way a single-geared EV accelerates from slow to high speed feels very familiar to us.
And whilst the near- 1000lb.ft headline torque figure from the Tesla sounds "whaaa??"

So could you use multiple gears in an EV?
Obviously yes, but more gears means more weight, complexity, and mechanical losses. In theory you could fit a 2-speed box running a higher gear at higher road speeds, which would drop the motor rpm back down into a "fatter torque" range, but the increased gearing (and additional losses) would probably make it feel little different in terms of "shove".
Some interesting points/comments in this vid (which I found after I'd been musing this for a while - doh
