Pre-heat the broiler. Toast half of the bread slices at a time on a baking sheet. Rub both sides of the toast with the sliced garlic and drizzle 1/2 cup EVOO over the slices.
While the bread is working, in a large skillet, heat the remaining 3 tablespoons EVOO, three turns of the pan, over medium-high heat. Add the onion and bell pepper and cook until slightly softened, 2-3 minutes. Add the broccoli florets and chicken stock and bring to a simmer. Cover the pan and cook until the broccoli is tender, about 8 minutes. Uncover and boil until the liquid evaporates, 1-2 minutes. Season, to taste, with salt and pepper.
In a medium size saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 minute. Whisk in the milk, bring to a boil, then lower the heat and simmer, stirring often, until thick and smooth, about 5 minutes. Season the sauce with salt, pepper and the nutmeg.
Pre-heat the oven to 450°F.
Layer half of the bread in a 9-inch x 13-inch casserole; spread with half of the broccoli mixture and top with the ricotta, a few ladles of the sauce and the Parmigiano Reggiano cheese. Layer the remaining bread slices, broccoli mixture, remaining sauce and all of the provolone cheese on top. Bake until brown and bubbling, 10-15 minutes.