Preheat the broiler and line a baking sheet with foil. Scoop out the seeds from the zucchini, leaving a 1/4-inch-thick shell. Brush the zucchini all over with 1 tablespoon olive oil and season with salt and pepper. Transfer to the baking sheet and broil until just soft, about 1 minute per side; set aside.
Meanwhile, bring a saucepan of salted water to a boil. Add the pasta and cook as the label directs; drain. Heat the remaining 1 tablespoon olive oil in a large skillet over medium heat. Add the shallot and cook, stirring, until tender, about 1 minute. Add the heavy cream and chicken broth, bring to a simmer and cook until slightly thickened, 5 to 6 minutes.
Add the havarti, 2 tablespoons parmesan, 1/2 teaspoon salt and a few grinds of pepper to the saucepan; stir until the cheese melts. Remove from the heat and stir in the egg yolk, pasta, parsley and lemon zest.
Combine the breadcrumbs and the remaining 1 tablespoon parmesan in a small bowl. Fill the zucchini halves with the pasta mixture and sprinkle with the parmesan breadcrumbs. Return to the broiler until golden brown, about 1 minute.