1/2 cup grated Parmesan cheese
If baking right away, heat the oven to 400 F. Coat a deep loaf pan with baking spray.
Use a bread knife to cut the loaf horizontally into thirds, creating bottom, middle and top layers. Set aside.
In a medium bowl, whisk together the eggs, milk, thyme, salt and pepper. Place the bottom layer of the bread in the prepared loaf pan. Drizzle about a third of the egg mixture evenly over the bread, then use a fork to gently press the bread all over to help it absorb the liquid.
Arrange half of the ham in an even layer over the bread. Top the ham with half of the turkey, followed by half of the cheese. Place the middle section of the bread over the ingredients, then use your hand to gently compress the bread and fillings. Drizzle another third of the egg mixture over the middle layer of bread, then press it gently with a fork to help it absorb the liquid.
Repeat the layering of ham, turkey and cheese, then top with the final layer of bread. Compress the bread and fillings as before, then carefully pour the remaining egg mixture over the top. Some will run down the sides between the bread and the pan; this is fine. Press the top of the bread with a fork the help it absorb the liquid.
Scatter the Parmesan cheese over the top of the loaf. Coat a sheet of foil with cooking spray, then use it to cover the pan. The stuffed French toast can be baked immediately, or refrigerated overnight.
When ready to bake, set the pan on the oven’s middle rack and bake for 1 hour, or until it reaches 155 F at the center. Uncover the pan and bake for another 5 minutes. Let cool slightly before serving.