Preheat oven to 425°. Line a large baking sheet with parchment, or two smaller ones.
In a large bowl, stir together all ingredients except the butter, fresh sage leaves, and Parmesan. Arrange in an even single layer on the sheet pan. If it seems too crowded, use a second pan for even cooking. Roast for 25-35 minutes, stirring halfway through.
While the gnocchi and veggies are roasting, make the brown butter. In a small skillet over medium to medium-low heat, melt the butter while whisking. Once it's melted it will become foamy and bubbly, whisk and continue to monitor until the foam dissipates, the color will turn golden brown, and the aroma will be very nutty. It may take a few minutes. If butter is not foaming or bubbling you may need to turn the heat up slightly. Once you reach the nutty brown butter stage, turn off the heat, and drop in the whole sage leaves. They will fry up and get crisp. Set aside off the heat until ready to use.
Drizzle about half of the brown butter over the cooked gnocchi and veggies, toss to coat. Garnish with the fried sage. Sprinkle with fresh grated parmesan cheese. Serve immediately. Any leftover brown butter can be kept in the fridge for up to a week, or freezer for three months.
If you're not a squash lover, try sweet potatoes or other veggies like cauliflower and broccoli.
Check out some other tasty uses for brown butter linked in this blog post. I like to make 2 whole sticks at a time so I have some on hand.