Butternut Squash and Sage Soup with parmigiano

2 1/2 lbs butternut squash, halved lengthwise and seeded 4 large eggs , plus 2 egg yolks 2 cups half-and-half 1 1/8 ounces finely grated parmigiano-reggiano[...]

1 tablespoon olive oil 1 onion (diced) 2 cloves garlic (chopped) 4 cups butternut squash puree (about 1 large butternut squash) 1/4 cup heavy cream (or Greek[...]