Grease a 9 x 13 inch casserole dish. Spread the bagel pieces evenly over the pan.
Crumble and cook the Italian sausage in a skillet over medium heat until no pink remains. Stir the sausage evenly into the bagel pieces.
In a large mixing bowl, whisk together the eggs, milk, salt, pepper, garlic, mustard, basil, and chives. Pour the mixture over the bagels. Cover with foil and refrigerate for at least 2 hours or overnight.
When ready to bake, remove the dish from the fridge and allow it to come up to room temperature while the oven preheats to 375 degrees.
Bake covered for 35 minutes, then remove the foil, sprinkle with cheese, and return to oven for an additional 10-15 minutes or until top is browned and cheese is melted. Let rest for 10 minutes before sprinkling with more fresh chives and serving.