Butter a 2-quart shallow baking dish (oval or square); set aside. In dish, alternately arrange, cut side down, muffin halves and Canadian bacon. Sprinkle with cheddar and Parmesan cheeses. Set aside.
In a large bowl, whisk together eggs, milk, mustard, 1/2 teaspoon salt, a pinch of pepper, and hot sauce until combined. Pour over muffins and bacon; cover tightly with plastic wrap. Refrigerate at least 2 hours and up to overnight.
Preheat oven to 350 degrees. Place baking dish on a rimmed baking sheet; remove plastic wrap. Bake until puffed and set in the center (see note below), about 1 hour and 30 minutes. (Tent loosely with foil if strata starts to brown too quickly.) Let stand 10 minutes before cutting and serving.
Let the strata chill 2 hours, and it will be nice and moist. If you leave it overnight in the refrigerator, it will be even more custardy.
To test for doneness, pierce center of strata with a sharp knife; it should feel firm and the knife should come out clean.
The muffin halves and Canadian bacon are arranged upright in the baking dish for easier serving. When cutting, you'll be able to see the layers and make sure each portion contains a few pieces of bread and bacon.