Cook the rotini. Bring a large pot of generously salted water to a boil. Cook the rotini according to the package directions until al dente. Drain and set aside.
Cook the squash. While the pasta cooks, heat 1 tablespoon olive oil in a large cast-iron skillet over medium-high heat. Add the butternut squash and cook, stirring occasionally, until tender and lightly browned. Season with salt, transfer to a plate, and set aside.
Brown the Brussels sprouts. Add another tablespoon of olive oil to the skillet if needed. Arrange the Brussels sprouts cut-side down and cook over medium-high heat for 3–4 minutes without disturbing them too much. Turn and cook for approximately another 5 minutes, until browned and tender. Season lightly with salt and transfer to the plate with the squash.
Brown the butter. Add the butter to the same skillet over medium heat. Cook, swirling occasionally, until it becomes golden brown and develops a nutty aroma. Watch carefully so it does not burn.
Add the aromatics. Briefly remove the skillet from the heat. Add the shallots, garlic, and marjoram and stir until fragrant, about 30–60 seconds.
Finish the sauce. Return the skillet to medium heat. Add 1/2 cup extra-virgin olive oil, lemon juice, lemon zest, and a pinch of salt. Stir until combined.
Add the pasta. Transfer the cooked rotini into the skillet and toss thoroughly until coated in the lemon brown butter sauce.
Season. Add black pepper, cinnamon, and nutmeg. Toss again so the warm spices are evenly distributed throughout the Fall Rotini Pasta Recipe with Butternut Squash.
Add the vegetables. Stir in the spinach and parsley, followed by the cooked butternut squash and Brussels sprouts. Cook over medium heat, stirring gently, until the spinach wilts and everything is warmed through.
Finish and serve. Transfer the pasta to a large serving bowl. Top generously with crumbled goat cheese and toasted pine nuts. Add a small drizzle of extra-virgin olive oil if desired and serve warm or at room temperature.