Butter a shallow 2-quart baking dish.
Arrange muffin halves and Canadian bacon cut sides down in dish.
Sprinkle evenly with both cheeses.
Whisk together eggs, milk, mustard, ½ teaspoon salt, a pinch of pepper, and the hot-pepper sauce until combined.
Pour into dish; cover tightly with plastic wrap. Refrigerate at least 2 hours (or up to overnight).
Preheat oven to 350 degrees.
Place baking dish on a rimmed baking sheet.
Bake until puffed and set in the center, about 1 ½ hours. (Tent loosely with aluminum foil if strata browns too quickly.)
Let stand 10 minutes before cutting and serving.
