Bipolar switched-mode power supply
I assume by your willingness to use an H-bridge that the Peltier device is electrically isolated; i.e. you don't have to have one end grounded.

If you know how to implement the slow H bridge that may be easiest.  Beware of strange switchover distortion effects if you're trying to go from heating to cooling (or visa versa) on the fly.

In theory, the most direct, least-component way to do it would be to drive that H bridge with a suitable pair of PWMs, and either control the output voltage or limit the duty cycles such that you stay within 12V.  But it'd probably have to be a BIG Peltier module for that to make sense.

If they're still made, an analog-input class D amplifier chip would work.