The day prior to serving, heat a heavy-bottom skillet over medium-high heat. Add the sausage and brown, about 8 to 10 minutes. Crumble the sausage into bite-sized pieces as it cooks.
While sausage is cooking, beat eggs, milk, ground mustard and kosher salt together in a medium sized bowl or large measuring cup.
Add bread cubes to a 9 by 13-inch casserole dish and top with browned sausage and shredded cheese. Mix to combine.
Pour the milk and egg mixture evenly over the dry ingredients. Press down on any of the bread cubes that are sticking up to ensure that they don't dry out.
Cover and refrigerate overnight. (This can be made the same day, just let it rest for an hour or two prior to baking).
Remove the strata from refrigerator and preheat the oven to 350°F.
Bake for 45 to 50 minutes until bubbly and brown. Remove and let cool for 10 to 15 minutes before serving.