Get a ridged griddle really hot; if you do not have one, heat an overhead grill.
Brush the leeks with olive oil, then place them on the griddle or in a grill pan and slide them under the grill.
Cook for 1 or 2 minutes, then turn.
Add the asparagus, brushed with oil, lower the heat and cook, turning occasionally till tender.
Check that the asparagus and leeks are cooked right through, then lift out and place on warm plates.
Sprinkle with salt and long, thin shavings of Parmesan.