Grease a 9-by-13-inch baking dish with butter, oil, or cooking spray.

Heat a large skillet over medium heat. Cook the breakfast sausage for 6 to 8 minutes, breaking it into crumbles, until browned and fully cooked. Drain excess grease and set aside to cool slightly.

Place half of the bread cubes in the prepared baking dish. Sprinkle half of the cooked sausage, 1 cup of cheddar cheese, and ½ cup of Gruyère cheese over the bread.

Add the remaining bread cubes, sausage, cheddar cheese, and Gruyère cheese in another layer.

In a large bowl, whisk together the eggs, whole milk, half-and-half, Dijon mustard, garlic powder, dried thyme, salt, and black pepper until smooth.

Pour the egg mixture evenly over the bread and sausage layers. Press the bread down gently with a spatula so it absorbs the custard.

Cover the dish tightly and refrigerate for at least 4 hours or overnight.

When ready to bake, preheat the oven to 350°F. Remove the dish from the refrigerator while the oven heats.

Bake uncovered for 45 to 55 minutes, until the top is golden brown and the center is set. A food thermometer inserted into the center should read 160°F.

Let the strata rest for 10 to 15 minutes before slicing. Garnish with chives or green onions, if desired, and serve warm.