Pour the olive oil into a shallow baking dish big enough to hold the asparagus in a single layer.
Place the asparagus in the baking dish (you may need to trim the woody ends to make them fit) and toss in the olive oil to coat.
Sprinkle with a little of the sea salt and all of the parmesan cheese, grated.
Place under the grill on about medium-high heat and put the asparagus underneath so the asparagus cooks through and parts of it brown up. The cheese should be bubbling and beginning to brown by the time the asparagus is cooked, anywhere between 5 and 10 minutes.
Remove from the heat and sprinkle with a little more organic sea salt and some cracked black pepper.