Can broccoli or cauliflower be canned/heat preserved?

As far as I know, it cannot. But due to prior knowledge I have also seen people do crazy things with vegetables and fruits, so canning might be a possibility, they aren’t very sturdy though, I think that is why manufacturers deter from them.

Freeze them.

In order to preserve either of these two vegs. it’s necessary to process them at really high heat for a long enough time to ensure that it won’t spoil.

Cooking them at high temps results in the release of all those noxious chemical elements which ensures they taste and smell like moldy old socks.

Would you want to eat that? I know I wouldn’t.

Is there a reason you haven’t considered freezing them? You can blanch cauliflower and broccoli and then freeze the vegetables.