Can I start to cook on a cast iron pan while it's smoking?
Yes, you can - for foods that are cooked at high temperatures, like steak, the oil is commonly heated until smoking anyways.
I suspect that the reason your pan is still smoking is due to the fact that you put too much oil when seasoning it - &quot;I'm reluctant to use the oven because the drips from the upside-down pan were far too messy&quot;. When seasoning your pan, all you need is the thinnest of coats, and if there is so much extra oil that it drips out, you should wipe most of it out. Having too much oil results in a sticky or tacky surface rather than a smooth patina, and even if you manage to polymerise such a thick layer of oil, it tends to chip off more easily.