Ingredients
Method
Place a rack in middle of oven; preheat to 425°. Whisk 1¼ cups all-purpose flour, ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, and lots of freshly ground black pepper in a medium bowl to combine.
Blend 5 large eggs, room temperature, in a blender on high until combined and frothy, about 1 minute. Add 1¼ cups milk, room temperature, then dry ingredients, blending to incorporate after each addition.
Place 4 Tbsp. unsalted butter in a 12" cast-iron or other ovenproof skillet. Set on a baking sheet and heat in oven until melted. Carefully remove pan from oven. Blend egg mixture 30 seconds (just to refresh the frothiness), then pour half of mixture into skillet. Sprinkle in half of 6 oz. sharp cheddar, coarsely grated, and half of 1 oz. Parmesan, finely grated. Pour in remaining batter, then top with remaining cheddar and Parmesan (the batter will not form layers, but adding in steps helps integrate some cheese deeper into the Dutch baby). Immediately return pan to oven (still on baking sheet) and bake until golden brown and puffed, 20–25 minutes. Let cool slightly (Dutch baby will sink as it cools).
While the Dutch baby bakes, clean blender and blend 1 garlic clove, finely grated, 2 cups (packed) mixed tender herbs (such as parsley, cilantro, mint, and/or chives), 3 Tbsp. extra-virgin olive oil, 3 Tbsp. fresh lemon juice, and remaining ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt until mostly smooth (some herb flecks are okay).
Place 3 cups trimmed arugula in another medium bowl and drizzle with dressing as desired; toss to coat. Serve Dutch baby with salad. (If you want to top the Dutch baby with the salad, serve immediately to keep the salad from wilting.)