How to stop steel cut oats from burning?

There are three factors when cooking oats or similar like cooked pudding or flan:

1. Stirring
   You have to be fairly diligent because if you do not stir constantly or at least in quite short intervals, the starchy mix near the bottom will stick. You need to "scrape" the entire bottom, not forgetting the outer areas or some streaks in the middle. This is somewhat connected to:
2. Heat
   The lower your heat, the lesser the risk of burning - simply because you have a bit more time until you need to stir up the layer closest to the pot's bottom. Less splatter is a nice side effect, too. If you initially bring your milk to a vigourous boil, you might still have too much residual heat even if you turn down your stove.
3. Sugar
   Yes, you didn't mention it, but in my observation adding sugar early during the cooking process might sweeten "the inner parts" of your oats better, but it heightens the risk of burning. Adding sugar at the end allows me to use less sugar for the same percieved sweetness as well.

You could also consider a non-stove technique like cooking them in a microwave, but you need to watch it closely the first few times to figure out the ideal power / timing combination for your serving sizes and microwave power, otherwise the oats have a tendency to "creep out" of your bowl and we're back at the "a pain to clean" stage. Soaking the oats overnight (-> overnight oats) can reduce the cooking time, because they are already soft.

I prefer steaming the oats in a bowl in the top of a pot with boiling water below and a lid on it.

No stirring, no boiling over. You would put oats and milk in a bowl, place on a rack in a steamer/large covered pot, and boil the water in the pot.

I don't recall ever getting a burnt layer before I tried this, but I cook them in water and add milk/cream/yogurt after they are cooked if adding milk/cream/yogurt - so the boiling milk could be part of your issue. Excess heat might also be part of the issue (usual reason for scorched/burnt layers of whatever on the bottom of the pot) - notably milk can burn, where water won't. But plenty of folk scorch rice in water with simply too much heat. You also don't mention stirring - which is essential when not steaming in my experience (which is a major reason why I now steam.)

Steel cut oats take much longer to cook, and because of all the starch and sugar the only way to avoid burning on the bottom is to either stir constantly at a higher heat or to reduce the heat to very low and cook them very slowly.

You can dramatically reduce the cooking time by soaking the oats overnight. When cooking oats of any kind much of the cooking time goes into hydrating the oats rather than cooking them, this takes much longer for steel cut oats as the shape of the cut oats gives it much less surface area. Soaking steel cut oats cuts down the time it takes to cook them from 25-40 minutes to 5-10 minutes. Some people eat them soaked without cooking but that's not everyone's taste.

You might find that adding the oats before heating the milk helps, and heating gently. But a lot of stirring is needed. Traditional Scottish recipes I've seen call for nonstop stirring.

Even a little water added to your milk also helps. If they start to thicken too much before they're fully cooked, a dash of cold water stirred in will help.

I usually cook oats in water, not milk. Perhaps you could use half milk, half water to avoid the burning? And lower the heat; it's time that softens the oats, not heat.