Zucchini (courgette) is very easy to prepare. Wash it thoroughly to remove any fertiliser or pesticide residue, which may not harm you but could kill fish. Cut it into thin slices about 5mm thick. Then score each slice - run the blade of the knife back and forth over each piece to crisscross it. It makes it easier for fish to break pieces off. Kind of like what you do to the cheek of a mango, only in minature.
The main problem with feeding zucchini is that it floats. The best option is to find something that sinks in the tank that has a thin edge. Use a clothes peg (plastic, not wooden because treated wood may leach into the tank) and clip the zucchini to that. Alternatively use a bulldog clip made of metal, which is heavy enough to sink a slice or two. You can also wedge it under something but I prefer not to, because it's hard for the fish to get at and they might dislodge it, then it just floats again.
Corys will eat almost any vegetable, they appreciate the treat but it's more required for vegetarian plecs (otos, bristlenose etc.) They prefer a larger range of vegies and most of those (such as pumpkin, potato and carrot) must be blanched or parboiled to soften them before the fish will show interest. Zucchini is so soft that this is not required.
EDIT: Syphoniera is dead right, if you cook anything too much it disintegrates in your tank, rots and produces a huge amount of ammonia.