In a large saucepan, heat the olive oil over medium-low heat. Add the shallot and cook until translucent, about 2-3 minutes. Add the butternut squash, season with salt, and let it brown lightly, cooking for about 4 minutes. Stir in the milk and add the reserved corn cobs. Bring the heat up to medium to let the milk simmer. Once the milk begins to bubble, let it simmer for about 5 minutes. Retrieve the corn cobs and discard. Transfer the butternut squash and milk into a blender and puree until very smooth. Set aside.
In the same saucepan, stir together the corn kernels and butter over medium heat. When the butter is melted through, stir in the pureed butternut squash and the mascarpone cheese. Lower heat and cook the corn, stirring periodically, until the sauce is creamy and the corn kernels are cooked, but still have some bite, about 10-15 minutes. Stir in the Parmesan cheese, and adjust the seasoning with salt and pepper if necessary.
Serve with a grating of Parmesan cheese and a sprinkling of fresh chives.
If you don’t have fresh corn, substitute with frozen corn. You will need about 3 cups.