Bring a large pot of salted water to a boil. Add spaghetti and butternut squash. Cook pasta al dente, about 10 minutes. Butternut squash should be fork tender and fully cooked at the same time. Strain and set aside.

Meanwhile, cook the bacon in a large pan or skillet over medium-low heat. Be sure to stir to prevent burning. Cook until just starting to brown, about 3-4 minutes. Remove from the pan and place on a paper-towel-lined plate to drain. Discard the majority of the bacon fat, leaving a little behind in the pan for flavor.

Melt the butter in the same pan. Add the garlic, thyme, brown sugar, cinnamon, and nutmeg. Heat for 2-3 minutes to let all the flavors soak together. Stir occasionally to mix.

Add the pasta, butternut squash, olive oil, and bacon to the saucepan. Toss with tongs to fully coat the pasta in the sauce. Top with pecorino romano cheese and parsley and continue to toss. Serve topped with shaved parmesan cheese and a little extra parsley.