In a large saucepan, bring 1 cup water to a boil. Add the spinach and cook until just wilted, 2 or 3 minutes. Drain and set aside. In a bowl, combine the eggs, yolks, and heavy cream. Season the mixture with salt and pepper and whisk until thoroughly blended. Add the finely crumbled goat cheese, chives, thyme, and Parmigiano. Set aside. Put the spinach in a kitchen towel and squeeze out all the moisture; you should have a ball measuring about 2/3 cup. Mince the spinach and add it to the custard. Blend well. Heat the oven to 375°F. If using a tart pan with a removable bottom, put it on a baking sheet. Pour the spinach and goat cheese custard into the prepared tart shell, being careful that it doesn’t overflow. Put the tart on a baking sheet and bake until the filling is nicely puffed and browned, 40 to 50 minutes. Let cool for at least 15 to 20 minutes before serving.