Preheat the grill. Place the asparagus in a saucepan of simmering water; cook until crisp-tender, 3 to 4 minutes. Drain well.
Place sliced bread on baking sheet. Grill 10 cm from heat until toasted, about 1 minute each side.
Spread 1 tsp mustard on each slice. Place 2 slices of ham, 6 thin or 3 thick asparagus spears, half a sliced hard-boiled egg, 2 tomato slices and a quarter of the provolone on top.
Grill open sandwiches until heated through and cheese is melted and golden brown, 1 to 2 minutes.
Choose spears of asparagus (green, white or purple) that are a bright, clear colour. Whether buying thin or thick asparagus, the stalks should be firm, full and round, with compact tips and tight scales. If the stalks are limp or bend easily, or the colour is dull, the asparagus is well past its best. Remove the tough ends of the stalks before cooking, keeping these trimmings to flavour a homemade vegetable stock.