Preheat oven to 350°F. Grease a 9×13-inch baking dish with nonstick cooking spray.
In a skillet over medium heat, cook the bacon until crispy, about 4–5 minutes. Using a slotted spoon, transfer bacon to the prepared baking dish.
In a small bowl, combine the mozzarella and white cheddar cheese. Sprinkle half of the cheese evenly over the bacon. Scatter the diced red bell pepper on top.
Arrange the croissant pieces over the bacon and peppers, allowing some edges to stick up for a golden finish.
In a large bowl, whisk together the eggs, milk, heavy cream, melted butter, Dijon mustard, Frank’s RedHot, salt, and black pepper.
Pour the custard evenly over the croissants, gently pressing them down so they absorb the liquid.
Sprinkle the remaining cheese evenly over the top. Then sprinkle with Everything but the bagel seasoning.
Bake uncovered for 40–45 minutes, until puffed, golden brown, and set in the center. If browning too quickly, loosely tent with foil after about 30 minutes.
Let rest for 5–10 minutes, garnish with fresh chives, and serve warm.