Heat 1 tablespoon olive oil or butter in a large, deep pot over medium heat. Add the breadcrumbs and toast for 3–4 minutes, stirring frequently, until golden brown.
Transfer the breadcrumbs to a bowl and let them cool slightly. Stir in 2 tablespoons Parmesan, the lemon zest and fresh basil. Season with salt and black pepper, then set aside.
Add the Italian sausage to the same pot. Cook over medium-high heat for 5–7 minutes, breaking it into bite-sized pieces, until browned and cooked through.
Transfer the sausage to a plate, leaving the rendered fat in the pot.
Arrange the sliced zucchini in the pot in a single layer. Add a little olive oil if the pot is dry. Cook undisturbed for 2–3 minutes, then flip and cook for another 1–2 minutes, until well browned. Season lightly with salt and transfer to a separate plate. Work in batches if necessary so the zucchini fries instead of steaming.
Reduce the heat to medium. Add the shallot and cook for 2–3 minutes, until softened.
Add the grated zucchini and a small pinch of salt. Cook for 4–5 minutes, stirring occasionally, until very soft and beginning to melt into the sauce.
Add the garlic, Italian seasoning and red-pepper flakes. Cook for approximately 30 seconds, stirring constantly.
Pour in the white wine and scrape up the browned bits from the bottom of the pot. Simmer for 2–3 minutes, until the wine has reduced by about half.
Stir in the Dijon mustard, then add the chicken broth.
Add the uncooked pasta and bring the liquid to a boil. Reduce the heat to a lively, uncovered simmer. Cook for 11–14 minutes, stirring thoroughly every 1–2 minutes so the pasta cooks evenly and doesn’t stick.
If the liquid is absorbed before the pasta is tender, add more broth or hot water ¼ cup at a time. When the pasta is al dente, the sauce should still look slightly loose.
Remove the pot from the heat. Stir in the heavy cream or half-and-half, ½ cup Parmesan and the butter until the sauce is smooth and glossy. Do not boil the sauce after adding the dairy.
Return the cooked sausage and browned zucchini to the pot. Fold everything together and let the pasta rest for 2 minutes. If the sauce becomes too thick, loosen it with a splash of warm broth.
Taste and season with salt and black pepper. Serve topped generously with the lemon-basil toasted breadcrumbs.