For the Bolognese, heat a large pot over medium-high heat. Place first 3 ingredients in the pot with a good drizzle of olive oil and cook for 5-7 minutes until caramelized. Season with salt and pepper.
Add beef and tomato paste, and cook for another 8-10 minutes. The mixture should be sticking to the bottom of the pot, but not burning.
Deglaze pot with red wine and stir all the fond off the bottom of the pot. Bring to a boil and reduce by half. Toss in chopped herbs.
Pour in tomatoes, crushing them inside of the pan, and bring back up to a boil. Reduce to simmer and let this cook until almost thickened, about 30-35 minutes. Adjust seasoning.
Stir in demi glace and cook for an additional 15 minutes until reduced and thickened.
For the Béchamel, heat the butter over medium-low heat in a medium saucepan until melted. Add the flour and stir until smooth. Over medium heat, cook until the mixture turns a light, golden sandy color, about 6-7 minutes.
Meanwhile, heat the milk and bay leaf in a separate pan until just about to boil. Add the hot milk to the butter mixture 1 cup at a time, whisking continuously until very smooth. Bring to a boil. Cook 10 minutes, stirring constantly, then remove from heat. Season with salt and nutmeg and set aside to cool to room temp.
Preheat the oven to 350°F.
In the bottom of a 9x13-inch deep-dish baking dish, add some Bolognese sauce to coat the bottom, spreading it out in an even layer. Arrange a layer of the lasagna noodles to completely cover the sauce. Spread a thin layer of the béchamel mixture over the pasta. Add some Grana Padano and Montasio cheese. Place another layer of pasta. And repeat this process, finishing with just béchamel and cheese at the top. This will give a beautiful golden cheese finish. Cover with plastic and then foil, this will keep a tight seal and keep the cheese from sticking to the foil.
Place the lasagna on a baking sheet and bake in the oven until the lasagna is hot and bubbly, about 1 hour and 15 minutes, removing the foil for the last 15 minutes of cooking. Let cool for 20 minutes before slicing.