Caramelized Onion Skillet Quiche

Name: Caramelized Onion Skillet Quiche
Ingredients: 1/2 (14.1-ounce) package refrigerated or frozen pie dough, thawed if frozen (or 1 homemade pie dough ); 3 medium yellow onions; 4 tablespoons (1/2 stick) unsalted butter; 1 1/2 teaspoons kosher salt, divided; 1 teaspoon freshly ground black pepper, divided; 1/4 cup finely chopped fresh chives; 4 ounces Gruyère cheese, finely grated (about 1 cup); 1 1/2 cups half-and-half; 6 large eggs; 2 packed cups baby arugula; Extra-virgin olive oil, for drizzling