Step 1

Preheat the oven to 450°F with a rack in the center. Set a 10-inch ovenproof skillet (cast-iron works best) in the oven to preheat at the same time.

Step 2

Combine milk, eggs, 1 tablespoon olive oil, the flour, ¼ cup Parmesan, and ¼ teaspoon salt in a blender. Blend on high speed until very smooth and the consistency of heavy cream, 1 minute. Set aside.

Step 3

Pour 3 tablespoons olive oil into the hot skillet and return it to the oven until the oil is rippling, 30-60 seconds.

Step 4

Pour batter into the hot skillet. Bake for 15 minutes.

Step 5

Meanwhile, as the Dutch baby bakes, prep the salad. Place the arugula in a large bowl. Add roasted red pepper, remaining ¼ cup Parmesan and ¼ teaspoon salt, the vinegar, and black pepper, and set aside (don’t toss yet). Flake the fish apart with your fingers, or separate into slices if it’s pre-sliced, and set aside.

Step 6

When the timer goes off, check on the Dutch baby. It’s ready when it’s puffed and slightly browned on top. Bake a few minutes longer if needed. Before taking the Dutch baby from the oven, quickly drizzle the salad with the remaining 3 tablespoons olive oil and give it a quick toss to combine. Taste the trout or salmon with a bite of the salad; if it’s quite salty and has enough vinegar, don’t season the salad more. If you’d like a little more flavor, toss the salad with a bit more salt and vinegar.

Step 7

Set a spoonful of the salad in the Dutch baby and sprinkle everything with paprika if you like. Cut the Dutch baby into wedges and place on plates. Divide the salad over the Dutch baby wedges, then top each portion with smoked fish. Serve immediately.