Preheat the oven to 350F/180C and toss the butternut squash and the tender stem with the olive oil and season with salt and pepper. Pick the needles of the sprig of rosemary and scatter over the tray. Roast in the oven for about 40 minutes until the squash and broccoli are golden and well roasted.
Bring a pot of salted water to a boil and cook the pasta according to the package directions. Reserve 1 cup of the pasta water before draining off. Meanwhile in a medium bowl, mix the grated parmesan, egg yolks, pinch of nutmeg and the heavy cream together.
Heat a medium skillet over a medium-high heat and add 1 tablespoon of vegetable oil. Once hot, add the bacon or lardons and garlic to the pan and cook until golden and crispy. Drain the pasta reserving 1 cup of the water and add the pasta to the pan with the bacon.
Add the cheese and egg mixture tossing quickly to prevent scrambling. *The heavy cream helps prevent this too. Toss the pasta until the cheese melts and a silky sauce forms. This should only take a minute. If the sauce is too thick, add some of the reserved pasta water to thin it out slightly.
Divide the pasta between 4 bowls and top with the pumpkin and broccoli. Serve with extra parmesan cheese.