Heat the oven to 350 degrees F. Place the diced baguette pieces and toast in the oven for about 10 minutes at 350 degrees.
In a skillet, melt the butter over medium heat. Add the pancetta, onion and celery. Cook until softened, about 5 to 8 minutes. Remove from the heat and add the vinegar. Stir and set aside.
In a large mixing bowl whisk the eggs. Add the green onion, diced ham, grated parmesan, grated Gruyere, chicken stock, pepper and salt to the eggs. Stir until all ingredients are incorporated into the mixture.
In a large casserole dish, place the baguette pieces into an even layer. Evenly pour the egg mixture over the bread. Stir to make sure the ham and cheese is spread throughout the casserole. Using the back of a spatula, press down on the top of the bread and egg mixture to create a flattened even top. Top with additional grated gruyere.
Place into the oven and bake until the casserole is set, about 45 minutes. Remove from the oven and let cool for 10 minutes. Top with freshly chopped basil, slice and serve warm.