Grate the zucchini into a colander using the large holes of a box grater. Toss with 1 tablespoon salt, then place in the sink to drain, about 15 minutes. Squeeze out the excess liquid.

Meanwhile, melt 4 tablespoons butter in a large saucepan over medium heat. Add the flour, nutmeg, cayenne, 2 teaspoons salt, and black pepper to taste and mix with a wooden spoon to make a paste. Cook, stirring, until the paste puffs slightly, about 3 minutes. Slowly whisk in the milk, then add the thyme, bay leaves and lemon zest and bring to a boil, stirring. Reduce the heat and simmer until thickened slightly, about 25 minutes. Strain into a bowl; discard the herbs.

Meanwhile, position a rack in the upper third of the oven and preheat to 425 degrees F. Bring a large pot of salted water to a boil; add the pasta and cook until al dente, about 8 minutes. Drain and add to the sauce.

Melt the remaining 4 tablespoons butter in a skillet over medium heat. Add the shallots and cook until translucent, 2 to 3 minutes. Add the zucchini and cook, stirring, until almost tender, about 4 minutes. Add the zucchini mixture to the pasta along with the egg yolks and all but 3 tablespoons of both cheeses; stir to combine, then add the spinach.

Transfer the mixture to a 9-by-13-inch baking dish and sprinkle with the reserved cheeses. Bake until browned on top and heated through, 25 to 30 minutes. Let rest 10 minutes before serving.

Photograph by Con Poulos