Preheat the oven to 400 degrees. Butter a 9-by-13-inch baking dish, and set it aside. Bring a large pot of salted water to a boil for the pasta.

Grate (on the large holes of a box grater) the bread into small crumbs; you should have about 1 cup. Melt 2 tablespoons of the butter in a small skillet over medium-low heat. Scatter in the crumbs, and cook, tossing frequently, until they’re light golden and crisp, about 3 minutes. Set them aside, and when they’re cool, stir in the Grana Padano.

To make the sauce: Melt the remaining 4 tablespoons butter in a large Dutch oven over medium heat. Once the butter is melted, whisk in the flour, and cook to toast it a bit, 1 to 2 minutes. Gradually whisk in the milk until the mixture is smooth. Add the bay leaves and 1 teaspoon salt. Bring to a simmer, and cook, stirring occasionally, until it’s thickened, 6 to 8 minutes. Reduce the heat to low, and stir in the Fontina, provola, and Taleggio, a few handfuls at a time, stirring until it’s smooth.

Meanwhile, add the pasta to the boiling water. Once the pasta is halfway cooked and still quite al dente, add the asparagus and peas, and cook until the pasta is al dente. Drain the pasta and vegetables, and add them directly to the sauce. Stir to coat the pasta thoroughly, and transfer the entire mixture to the prepared baking dish. Sprinkle with the crumbs. Bake until the edges are bubbly and the top is golden brown, 40 to 45 minutes.