For the onions: Preheat your oven to 325 degrees F (160 degrees C). Scatter the onions onto a rimmed baking sheet along with the garlic and thyme. Drizzle with the olive oil, brandy and maple syrup. Season with salt and pepper and toss to combine. Cover tightly with foil and transfer to the oven for 2 hours.
Remove the foil and stir in the vinegar. Return to the oven for 15 to 20 minutes, or until caramelized. Season to taste with more salt and pepper, if needed, and set aside.
For the sandwiches: Set your broiler to low and line a baking sheet with foil. In a small saucepan, heat the milk over medium-low, until steaming.
For the mornay sauce, melt the butter in a medium saucepan over medium heat. Sprinkle in the flour and cook, whisking, for 1 minute. While whisking, slowly add the milk. Add the salt, pepper, herbes de Provence and freshly grated nutmeg. Bring to a simmer and cook, stirring occasionally, for 1 to 2 minutes, until thickened. Remove the sauce from the heat and whisk in the Parmigiano-Reggiano and 1/4 cup of the Gruyère or Emmental.
Lay half of the bread out on the prepared baking sheet and spread 1 teaspoon of Dijon over each slice. Top each with two slices of ham, if using, about 3 tablespoons caramelized onions and divide half of the cream sauce over top. Scatter about 2 tablespoons of the grated Gruyère or Emmental over each and sandwich with another piece of bread. Spread the remaining cream sauce over the tops of each sandwich and scatter over the remaining cheese.
Broil the sandwiches for 4 to 6 minutes, or until golden brown and bubbling.
Meanwhile, fry the eggs in a little butter over medium-high heat until crisp around the edges, leaving the yolks runny.
Top the sandwiches with the fried eggs, scattered with a few fresh thyme leaves and season with some extra salt and pepper.
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