Heat olive oil in a large skillet over medium heat. Add onion and cook, stirring frequently, until lightly browned, about 3 minutes. Add garlic and cook until fragrant, about 1 minute.

Add mushrooms and cook, stirring occasionally, until browned and most of their liquid has cooked off, about 8 minutes. Remove from the pan and wipe the skillet clean. Set the mushroom mixture aside.

Return the skillet to medium heat, add bacon, and cook, stirring frequently, until crisp, 6 to 8 minutes. Drain the fat and transfer bacon to a paper towel lined plate.

Stir the bread cubes, mushroom mixture, bacon, and smoked cheddar into the egg mixture until evenly combined. Season with black pepper.

Pour the mixture into a 9x13" baking dish. Cover with foil and refrigerate at least 8 hours or overnight, so the bread has time to soak up the egg mixture.

When you're ready to bake, preheat oven to 350F and let the strata sit at room temperature for 20 minutes to take the chill off.

Bake uncovered until puffed, set in the center, and golden brown on top, 40 to 45 minutes. Let rest 10 minutes before serving.