You'll likely run into problems trying to do that with a modern toaster.

The last few I've seen in bits use a resistive tap off the heating element to provide 12v power for the control PCB.

If you reduce the power to the heating element (by whatever means - triac dimmer, Variac etc) you'll proportionately reduce the 12v going to the control PCB.

A small change in voltage won't be a problem, but if you're going to aim for 50% or the like, the control PCB won't work, and the latch function which holds the mechanism down won't work, so no power at all to the element, no toasting.

If you were going to go all-out, then a triac type lighting dimmer with sufficient power handling (my guess is 1kw - 2kw depending on the toaster size), and an external 12v transformer for the control board would do it.

This would be tricky to fit within the limited spare space in the housing.