Place a 9 x 13-inch baking pan on the bottom rack of the oven. Fill it halfway with water to create steam while baking. Preheat the oven to 300℉.
Prepare a muffin tin with at least 8 wells and spray each well thoroughly with non-stick cooking spray or brush olive oil evenly (I use a silicone brush).
Add the egg whites to a large bowl and whisk for about 30 seconds, until light and frothy. Reserve ¼ cup of the shredded Gruyere cheese and add the remaining cheese to the egg whites. Stir in the finely chopped broccoli, Parmesan cheese, salt, and black pepper until combined.
Divide the egg filling evenly among 8 prepared muffin wells, using a spoon to distribute the broccoli and cheese evenly in each.
Bake for 20 minutes. Carefully sprinkle the tops of the bites with the reserved Gruyere cheese. Return to the oven and bake for about 10 more minutes, until the egg bites have puffed slightly and are cooked through in the center.
Remove from the oven and let cool in the pan for 5 minutes before carefully removing and serving.