Preheat the oven to 400°F.
Bring a saucepan of lightly salted water to boil.
Trim the asparagus and peel it, leaving the tips and about 1 inch unpeeled.
Reserve the peels.
Place the asparagus in the boiling water, reduce heat and simmer for 7 minutes.
While the asparagus is cooking, grease a gratin dish liberally with butter.
When the asparagus is done, drain and arrange in the gratin dish. Set aside.
Place asparagus peels, thyme, and bay leaves in a small saucepan. Add milk, bring to a boil, then remove from heat and set aside to steep for 10 minutes.
In a medium saucepan, melt butter over medium heat.
Add the flour and cook for 1 minute. Strain the herbed milk into the butter and flour mixture, and cook over medium heat until béchamel sauce is thick.
Season with salt and pepper, and stir in Parmigiano-Reggiano.
Pour the béchamel over the asparagus.
Melt the truffle butter in a small skillet; crush the cracker crumbs and add to the butter. Season well with pepper.
Cook a minute or two, until the cracker crumbs take on some color.
Sprinkle them over the béchamel sauce, and bake for 20 minutes until bubbling and golden.