Arrange asparagus in a grill basket in a single layer, drizzle with olive oil.

Grill over low heat, tossing occasionally until tender and some pieces are slightly charred, 8 to 10 minutes.

Remove from heat and carefully transfer to a cutting board, chop into 1/2 inch to one inch pieces.

In a small saucepan bring balsamic vinegar to a boil, reduce heat and simmer until thickened and reduced by half.

Toss the chopped asparagus with the balsamic glaze.

On a performed pizza pan or rimmed heatproof baking dish, arrange the nachos, top with cheddar, asparagus and chopped tomatos.

Place the pan on the grill over low heat, close the lid and heat for 4 to 5 minutes (checking every couple of minutes) until cheese is melted.

Carefully remove from heat and immediately sprinkle with grated parmesan.