You must have a really high-BTU cooktop; most of them have a "simmer" setting that I guess yours doesn't have . Cast iron would be the best heat diffuser, I would think. That's what I have, although I haven't used it since we got our new cooktop that goes very low as well as very high (my LeCr is fine on it).
If you're afraid of butter, use cream. ~~ Julia Child
As you cook, you enjoy omniscience about food that no amount of label reading can match. Having retaken control of the meal from the food scientists, you know exactly what is in it. (Unless you start w/cream of mushroom soup, in which case all bets are off.) To reclaim control over one's food, to take it back from industry & science, is no small thing; indeed, in our time, cooking from scratch qualifies as subversive. ~~ Michael Pollan