In a large pot of boiling salted water, cook pasta according to package instructions; drain well.
Melt butter in a large skillet over medium heat. Add garlic, mushrooms and onion. Cook, stirring occasionally, until tender, about 3 to 4 minutes. Stir in thyme and dill until fragrant, about 1 minute; season with salt and pepper, to taste.
Whisk in flour until lightly browned, about 1 minute. Gradually whisk in vegetable broth, and cook, whisking constantly, until incorporated, about 1 to 2 minutes. Stir in half and half until slightly thickened, about 1 to 2 minutes.
Stir in baby spinach and Parmesan until the spinach has wilted, about 2 minutes. If the mixture is too thick, add more half and half as needed.
Stir in pasta and gently toss to combine.
Serve immediately, garnished with parsley, if desired.