The easy version would be to feed it 5V current
You could cut or de-solder the ribbon cables and power the upper board alone connecting the +5V and GND wires on the left ribbon to an appropriate power supply. If the upper board isnt blown you might be able to get it to work.
This kind of two board design is quite common. The bottom PCB is a mixed high + low voltage board that includes the mains power supply with bridge rectifier, transformer and smoothing caps. It sends low voltage power to the upper board via the ribbon.
The upper board is entirely low voltage and has a microcontroller, display, buzzer and the control knob. Sensors and switches in the oven are passed over the ribbon to the controller, and control signals are passed back through the ribbon to the relays on the power board which then switch high voltage power to bulbs, fans, and other stuff.
As long as you don't connect it to mains power it's a safe low voltage in this case, there is nothing on this board that will generate high voltage from 5V. Don't leave it powered when you're not there, low voltage can still burn your house down!
The more complicated version would be to also reprogram the chip
This is unlikely, but you never know. Its probably a custom pre-programmed chip that can't be erased, or at the least it has been locked so it can't be modified or have the software read out. It's possible that it could be programmed in place on the board without de-soldering.
Interestingly the upper PCB also seems to have something that looks like an SPI port (P21) it's possible this controls something in the oven but I doubt it. It could be a programming interface but SPI is not typically used for that, maybe a test interface? Hard to say. (edit on 2nd thoughts it probably is a programming interface)
Someone with good electronics / software skills could replace it with an equivalent blank programmable CPU and program it (with something), but that would be a big project even for experienced engineers. Mostly the lack of detailed info about the hardware usually makes it easier to design something new from scratch than to reverse engineer somone elses design.
WKP - might mean wake up. SDA - serial data out SCL - serial clock RST - reset GND, 5+V - power and ground
Ok so it will be talking to another chip on the keyboard PCB. Not a programming interface.