My shot recovery time is currently 3 minutes.

The PID is set to 220F.
P=1.8
I=60
D=15

The machine is 1 year old. I descaled @ 8 months. I say this because I heard older machines with scale build up could have poor recovery time.

For what its worth I can get up to 220F very quickly (in seconds) when I flip the steam switch..

Simply warming up my shot glass with 1oz of water results in a 1 minute recovery.

Is something wrong or is this normal?

wot PID?
P/I/D values have different meanings on different PID

I have the auber kit with steam & pre-infusion. Not sure of the exact model of the controller.

For the Auber :
P = % of range. What type of Sensor? RTD, K, T ? Assuming an RTD and temperature sense code P10.0 [range -99.9 to 999.9°F ~1100°F], a setting of 1.8 = 1100*.018 or ~20°F. This maybe too wide a band for quick control.

I = 60 sec : lower this number to make response faster

D = 15 sec : to low or too high can make system unstable. Common setting is I x 25%

If you feel comfortable, list the parameters from the instruction manual that affect performance.

Also see http://www.expertune.com/tutor.html

My shot recovery time is currently 3 minutes.

Not enough info.
Is it a single (1oz), double (2oz) or triple (3oz)?
Do you pre-flush or draw from the boiler in any other fashion?
For example, is your "warming up my shot glass" part of this routine? On a small SB machine, that IS a big deal. If you must warm cups, I suggest using other means, such as your kitchen faucet, a kettle, microwave or the top surface of the Silvia (weak as that is). Or run boiler water into your cup, then wait for recovery, then pull your shot.

For what its worth I can get up to 220F very quickly (in seconds) when I flip the steam switch..

Sure you can, but not without overshoot; that's why we fork over the $$ for PID. To appreciate the magnitude of the overshoot, try this, but turn off the steam switch at 220F and watch how far it rises before peaking. On the plus side, this suggests your element is good and not scaled.

Simply warming up my shot glass with 1oz of water results in a 1 minute recovery.

This would be more meaningful if we knew the size of the excursion, but it sounds in the ball park to me. Strictly from memory, I had a 2-minute recovery for a double (2oz), which I ran without any sort of pre-flush, which would defeat the whole purpose of the PID. With a reasonable set point and a fully warmed group (including PF), you are good to go as soon as recovery is indicated.