Savory Dutch Baby with Arugula Parmesan

Name: Savory Dutch Baby with Arugula & Parmesan
Ingredients: 7 large eggs, divided; ⅔ cup whole milk; ¼ cup all-purpose flour; ¼ cup whole-wheat pastry flour; ½ teaspoon kosher salt; ½ teaspoon ground pepper, divided; 3 tablespoons unsalted butter; 2 tablespoons extra-virgin olive oil, divided; 2 teaspoons lemon juice; 2 ½ cups baby arugula; 1 ounce Parmesan cheese, shaved