Heat oven to 435F and line a large sheet pan with parchment paper. Rinse and chop broccoli into large bite size pieces. Pile the broccoli on the lined sheet pan, drizzle the olive oil over, and sprinkle with the garlic powder. Massage briefly to distribute oil and garlic powder. Place in the top third of the oven.
While the broccoli is roasting, dice your onion. Melt 1 tablespoon of butter in a medium sauce pot. Over medium heat, stirring often, cook onions until translucent and well browned without burning. Scrape out onion into a medium mixing bowl and set aside.
Put a large pot of salted water on to boil for your lasagna noodles. Check broccoli, once dark brown in places, remove from the oven on a trivet to cool to handle.
In the pot you cooked the onion, melt the remaining 3 tablespoons of butter on medium-low heat and sprinkle in the flour and thyme. Whisk for a few minutes to cook the flour and warm the two cups of milk in the microwave (a minute to a minute and a half).
Turn the flour and butter mix heat down to low, pour in a scant two tablespoons milk (eyeball, measurement not necessary) and whisk vigorously. The flour paste will almost immediately absorb the milk and thicken. Pour in two more tablespoons, whisk vigorously. Keep repeating with small amounts of milk, making sure to clear any clumps from the center of your whisk until the milk isn't immediately absorbed. Increase to about half a cup of milk, whisking in between, until all milk has been added. The bechamel will be thin, this is good!
Crumble in the blue cheese and whisk to make your blue cheese bechamel. Set aside 3/4 cup of the blue cheese bechamel for final topping of the lasagna.
Take the cooled, roasted broccoli and finely chop. Or give a brief run through a food processor if you have one. You want less than 1 cm pieces so that your layers are not lumpy, but not a puree. Mix the chopped roasted broccoli into the blue cheese bechamel. Taste for salt as many strong cheeses are quite salty and then add more salt if needed.
Add the ricotta, black pepper, and about 2 teaspoons of salt, and mix in with the cooked onion. Taste for salt before adding the two eggs. Add more salt if needed and then add the eggs. Stir well.
Just before assembly, lightly oil a 9x13 casserole dish, and drop lasagna sheets in your boiling salted water for 2-3 minutes to just soften. Drain the sheets and cut noodles as needed to make a single layer in the bottom of the dish. Dot the first layer of pasta with half the blue cheese bechamel and broccoli mixture. Carefully spread into a thin layer.
Layer with more pasta. Dot the layer with half of the ricotta mixture. Carefully spread into an even layer. Repeat once more with each filling mixture. Top with the 5th and last layer of pasta. Spread with the plain blue cheese bechamel that was set aside. Cover with foil and place in the oven for 25 min. Bake on a lipped sheet pan to prevent possible splatter issues.
Carefully peel the foil off, sprinkle the Parmesan or other cheese on, crank the oven up to 450F and place the rack in the top of the oven for 10 min or until browned. If the cheese is not browned and crusty after 10 min, turn on the broiler and carefully watch. Cool for 10 min before slicing. Serve with a salad dressed with an acidic vinaigrette.