Heat olive oil in a frying pan over medium-high heat.
Add turkey sausage and cook, breaking into small pieces, until browned and cooked through; let cool slightly.
In a large bowl, whisk together the eggs, half-and-half, dry mustard, salt, and pepper.
Grease a 9×13 baking dish.
Spread the cubed bread and browned turkey sausage evenly across the bottom of the dish.
Sprinkle the shredded sharp cheddar cheese over the top.
Pour the egg mixture over the bread, sausage, and cheese.
Cover and refrigerate for at least one hour or overnight to allow flavors to meld.
Preheat oven to 350°F.
Bake the casserole for 55 minutes until the center is set and the top is golden brown.