Preheat the oven to 425 degrees F. Heat the olive oil and butter in a large skillet over medium-high heat. Add the garlic and cook until softened, about 1 minute. Add the greens and 1/2 teaspoon salt; cook, stirring occasionally, until the greens wilt and most of the liquid evaporates, 5 to 7 minutes.
Meanwhile, roll out the puff pastry on a lightly floured surface until large enough to fit in a 9-inch pie plate. Ease into the pie plate and trim the edge; crimp if desired. Scatter the goat cheese and parmesan in the crust, then top with the sauteed greens.
Whisk the eggs, heavy cream, nutmeg, 1/2 teaspoon salt and 1/4 teaspoon pepper in a medium bowl; pour over the greens. Bake until the crust is golden brown and the quiche is set, about 20 minutes. Slice into wedges.
Photograph by Christopher Testani
Courtesy of Food Network Magazine