Voltage surge during transition of high side mosfet in half bridge mosfet gate controller
D1 (1N4001) is inadequate. This diode is for rectifying 50 Hz, not 32kHz. Please select an appropriate fast rectifier (schotty or standard, doesn't really matter, but aim for a fast recovery time).

Decoupling is insufficient. Both +36V and +12V need proper decoupling.

Power rail (+36V) needs low-ESR capacitor(s) plus MLCC for HF decoupling.
Driver rail (+12V) needs MLCC as close to the chip as possible. Add aluminium cap if necessary for regulator stability.

Also, the glitch appears on the input PWM too, which means it is a measurement artifact, probably a grounding issue, either due to induction into long scope's alligator clip wire, or shared ground paths on breadboard.

Now, this is on breadboard, so you can expect poor transient behavior. Do a proper layout (we can help) and it should be OK.