Lightly grease an 11 x 7-inch baking dish.

Heat the oil in a large nonstick skillet. Add the sausage, stirring often, until the meat is browned and cooked through, about 5 minutes.

Line the baking dish with overlapping slices of bread.

Spoon the sausage on top of the bread. Sprinkle evenly with the cheese.

Crack the eggs into a large bowl. Then use a fork to stir together the eggs, milk, and mustard until smooth. Pour over the bread mixture. Cover and refrigerate for at least 4 hours or overnight.

To bake, preheat the oven to 350 deg F. Bake the strata, uncovered, until the top is puffed and browned and a toothpick inserted in the center comes out clean, about 45 minutes. Remove the dish from the oven and let stand for 15 minutes before serving.