Not sure if this has been scientifically studied but I’ve noticed a couple situations where continuous heat can be avoided.

My mom’s way of cooking corn on the cob: bring a pot of water to boil, lid off with two wooden spoons resting on the top to prevent boiling over. She keeps the heat continously quite high for what, ~30—40 min? Seems wasteful because with the lid off the pot is evaporative cooling the whole time so more heat is needed to offset the cooling. I just tried it this way: bring to boil with lid on. Shut the burner off as soon as it boils. The corn continues cooking as the water temp drops. I could probably improve on that even more by using a pressure cooker. (I’m stalling on buying one because I boycott InstantPot due to the fact that they have a closed source phone app exclusively in Google Playstore; it’s optional but InstantPot buyers are still financing that. I should probably get a 2nd hand manual pressure cooker).

Hydrating dried beans: soak overnight (which I skip because it seems to make little progress). So I do the “quick soak” – bring to boil with lid on, turn off right away, and let them sit ½ the day in warm water. Pressure cooking speeds up the 2nd stage cooking for sure (I’ve tested with other people’s pressure cookers). Since I don’t have a pressure cooker, I end up doing the quick soak method ~3 or 4 times throughout the day… which just means bring to a boil then shut off. Anecdotally this seems to reduce the time needed in the final phase of cooking.

Am I going OCD on this? This all might be a drop in the ocean… cooking is not a significant portion of energy consumption. But maybe notable in the summer when cooling systems have to work against the kitchen heat. Which is one reason I like the electronic pressure cookers: I can set the pressure cooker outside.