Cook the asparagus spears in boiling salted water for 3 minutes, toss with the thyme leaves and season with salt and pepper. Reserve on a plate.
Brush the slices of bread with olive oil, lay 4 of them on a work surface, top each with 2 slices of Mozzarella cheese, follow with 8 asparagus spears and a final slice of Mozzarella.
Warm a non stick frying pan over medium heat and grill the sandwiches 3 minutes per side or until they are golden brown and the cheese is melted.