Break the broccoli into small florets by hand, and chop the stem into small pieces.
Bring a small pot of water to a boil. Add salt then add the broccoli and boil for about 7 minutes, or until tender, with the lid on.
While the broccoli is cooking, heat a generous amount of EVOO and a splash of water in a large pan over medium-high heat. Add the chopped onion and sauté for 5 minutes or until it starts to soften, mixing often with a wooden spoon.
Add a splash of wine, stir, then add the sliced mushrooms, butter, and chopped parsley. Mix well, then add the ground beef, using a wooden spoon to break it up into smaller pieces and combine everything evenly as it cooks.
Season with salt and pepper, then once the beef starts to brown, add the rest of the wine and let it simmer until the excess liquid evaporates.
When the broccoli is done, drain it and add it to the pan with the beef and mushrooms. Lightly mash the broccoli into the mixture to help it blend, being careful not to squash them into a puree. Tear the basil leaves into small pieces and sprinkle them in. Turn off the heat and set the filling aside.
Place a deep, small pot over medium-low heat and add 50g of butter. Let it melt slowly, then whisk to combine.
Add the flour and stir until fully incorporated then begin adding the milk a small amount at a time, whisking constantly.
Continue adding the milk gradually and each time the mixture thickens, pour in a bit more and keep whisking. Take your time and lower the heat if it helps with the process, trying not to avoid or smooth out any lumps.
Once all the milk has been added and the sauce is smooth and creamy, add a pinch of nutmeg and stir to combine. Turn off the heat and give it one final whisk to keep it lump-free.
Start by spreading a thin layer of béchamel on the bottom of your baking dish. Add a spoonful of the beef and broccoli filling, then place your first lasagna sheet on top. Press down gently to help it settle.
For the next layer, spread more béchamel, then add a generous amount of the filling. Sprinkle over diced provolone, mozzarella, and a bit of grated pecorino. Add a small drizzle of béchamel on top, then cover with another lasagna sheet. Press lightly again.
Repeat the process for the third layer. This time, make it extra generous, since it’s the center of the lasagna. Layer with béchamel, plenty of beef and broccoli, the cheeses, and then another sheet of pasta.
Keep layering until you’ve used up the filling. Be sure to press each layer down slightly to compact the lasagna, and remember to save a good amount of béchamel for the final top layer.
Once you’ve added the last pasta sheet, cover any gaps and press down gently. Spread the remaining sauce all over the top, from edge to edge.
Cover the dish with foil (making sure it doesn’t touch the sauce) and bake at 180°C / 356°F for 20 minutes.
After this time, remove the foil and add a final layer of provolone, mozzarella, and grated pecorino on top. Bake for another 10 minutes uncovered at the same temperature, or until the top is golden and bubbly.
