Preheat oven to 400 degrees F.
Place the chopped butternut squash on a parchment lined baking sheet.
Drizzle with olive oil, a dash of salt and pepper and bake for about 15 to 20 minutes or until fork tender.
Set the cooked butternut squash aside while continuing with the rest of the recipe.
Butter a 9 inch springform pan with softened butter.
Sprinkle the pan all over with 1/3 cup of grated Parmesan cheese and set aside.
In a large saucepan, melt 1/4 of the butter over medium heat.
Add the all purpose flour to the melted butter and cook while whisking for 2 minutes.
Slowly whisk in the milk.
Reduce the heat slightly and let he sauce simmer while whisking often, until the sauce has thickened, for about 20 minutes.
Remove the saucepan from the heat and whisk in the Asiago cheese and 1 cup of the Parmesan cheese.
Whisk in the lightly beaten egg and season with salt and pepper.
Cover the saucepan and keep warm.
Preheat the oven to 375 degrees F.
Bring a large pot of salted water to a boil and cook the pasta just until al dente or firm to the bite.
Drain the pasta and transfer to a large bowl.
Add the cooked butternut squash, arugula, parsley and rosemary to the pasta bowl.
Stir in the cheese sauce until well combined.
Transfer half of the pasta mixture to the prepared springform pan.
In a small bowl, mix together the ricotta cheese and lemon zest then spoon half over the pasta.
Transfer the remaining pasta into the pan and spoon the remaining ricotta mixture over the pasta.
Sprinkle with 1/2 cup of grated Parmesan cheese and bake for about 45 minutes or until the top is golden brown.
Let the baked pasta rest for about 1/2 hour before releasing from the pan.
Cut into wedges and serve.