Holy hell, you are in a mecca of tastiness. Do you have a dutch oven? Go to any of the flea markets and grab one and you are good to go as you can braise away on your hot plate. If you have the funds get a blowtorch - cooking or a regular one. When I didn't have an oven that was my trick for crisping up steamed potatoes and pretty much anything else I wanted to hit with fire. Steaming and poaching is your friend - add aromatics to the liquid, season differently and you can make it all work. Slice, shred, cube. Chicken salad, add to stir fries, top greens. Make little tacos and put into lettuce leaves, do this with beef pork chicken. Braise cheap cuts of meat and pick away. Sear steak. Smash and steam all varieties of tubers. Take the smashed potatoes and make a potato pancake all nice and crispy, top with a protein and poached eggs. I made pigeon in red tea when I was there last and it was all stove top. You can totally make a big frittata on the stove, cover with the lid so it steams all the way through and is cooked firmly. Hit with the blowtorch to give colour on top. Slice what you want to eat and throw the rest in the fridge for later. Was just thinking you could do a pot of mussels with herbs, white wine, butter, etc., and since there's no bread to mop up the delicious cooking liquid, save it and make a killer fish soup the next day.
For a sweet make puddings out of dark chocolate and coconut milk unless you're eating dairy, then the world of treats is wide open. You can make little steamed cakes, too! And don't stay too far away from fruit, wild Gariguettes make me swoon.
I should probably stop now :) Have fun!