Preheat the oven to 325 degrees F.
Separate the eggs (save the yolks for another recipe like my keto ice cream, hollandaise, mayo or lemon curd), and place the whites into a large CHILLED bowl or stand mixer (if the bowl is warm, it activates the gelatin and will gum up). Add the allulose, gelatin, salt and cream of tartar if using and whip the whites for a few minutes until VERY stiff.
Turn the mixer to low and gently mix the egg white protein powder into the whites.
Note: If adding yolks, lightly combine. But note, the yolks will increase fat and can increase likelihood of falling.
Grease a bread pan with avocado oil spray and fill with Chewy Protein Sparing Bread mixture.
Bake for 30 minutes or until golden brown. Turn oven off and leave bread in the oven for 15 minutes to avoid the bread from falling.
Let completely cool before cutting or the bread will fall. Cut into cubes and set aside.
To make the Croque Monsieur Bread pudding, place the butter flavored coconut oil into a skillet over medium high heat. Add the chopped onions and saute for 3 minutes. Add the garlic and thyme and saute another minute. Remove from heat and set aside.
In a large bowl, place the eggs, cream, broth, Dijon, hot sauce, and salt. Stir well to combine.
Spray avocado oil spray into a 11 by 7 inch baking dish. Place half of the cubed bread into the dish. Top with half of the shredded Gruyere cheese, diced ham and half of the onion mixture. Repeat with another layer of bread, cheese, ham and onion mixture. Pour the egg mixture into the dish to cover the bread. Cover and refrigerate for 3 hours or overnight.
When ready to bake, preheat oven to 325 degrees F. Bake for 30 minutes, then remove from the oven and sprinkle the Parmesan on top and increase the temperature to 375°F. Bake for another 15 minutes or until Parmesan is golden.
Remove from oven and allow to sit for 5 minutes before slicing. Serve with hot sauce if desired.