Heat a large skillet over medium heat. Add the ground spicy Italian chicken sausage and cook, breaking it up, until browned and cooked through, about 5 to 8 minutes.
Add the chopped shallot, chopped garlic, dried oregano, and dried thyme to the skillet and cook, stirring, until fragrant and the shallot is softened, about 2 to 3 minutes.
Stir in the chopped oil-packed sun-dried tomatoes and cook for 1 to 2 minutes more.
Pour in the low-sodium chicken broth and stir in the Dijon mustard, then bring the mixture to a boil.
Add the dry orzo and shredded zucchini to the boiling broth. Reduce heat to a simmer and cook, stirring frequently, until the orzo is al dente and most liquid is absorbed, about 6 minutes (or as the package directs).
Stir in the fresh baby spinach until wilted, then pour in the coconut milk or heavy cream and sprinkle the grated Parmesan over the top.
Stir continuously until the sauce is creamy and cheese is melted, then remove from heat. Serve topped with fresh basil.