Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Add the gnocchi, green beans, pancetta, red pepper and onion to a large bowl and mix to combine. Spread the gnocchi mixture in a single layer on the prepared baking sheet and sprinkle with the salt and pepper. Cut 4 tablespoons of the butter into pieces and top the gnocchi mixture with the butter pieces and sage leaves. Place on the middle rack and bake, stirring halfway through, until the gnocchi are tender, 16 to 18 minutes.
Melt the remaining 2 tablespoons butter and keep warm. When the gnocchi are tender, drizzle the mixture with the butter and gently stir to combine with a rubber spatula. Scoop the mixture into a large serving bowl and garnish with the Parmesan and basil.