Mushroom and Onion Dutch Baby

Ingredients

• 3 large eggs, at room temperature
• 3/4 cup milk, heated in microwave for 30 seconds
• 3/4 cup white whole-wheat flour
• 1 teaspoon kosher salt, divided
• Freshly ground black pepper
• 3 tablespoons unsalted butter, divided
• 1 medium onion, sliced thinly into half-moons (about 1 cup)
• 8 ounces sliced mushrooms (about 3 cups)
• 2 tablespoons minced fresh chives
• 1/2 cup grated Parmesan cheese (about 2 ounces)