Step 1

Dice 1 large shallot (about 1/2 cup). Finely chop 3 garlic cloves. Cut 1/2 medium lemon into 4 wedges and reserve for serving.

Step 2

Prepare the following, adding each to the same small bowl as it is completed: Finely grate the zest of the remaining 1 medium lemon until you have 2 teaspoons. Juice the lemon until you have 3 tablespoons. Pick the leaves from 8 fresh parsley sprigs and coarsely chop (about 1/4 cup).

Step 3

Pat 4 (about 5-ounce) trout or salmon fillets dry with paper towels. Season all over with 3/4 teaspoon of the kosher salt and 1/4 teaspoon black pepper.

Step 4

Heat 1 tablespoon of the olive oil in a large straight-sided skillet or nonstick frying pan over medium-high heat until shimmering. Working in batches if needed, add the fish in a single layer skin side-up. Sear undisturbed for 3 minutes. Carefully slide a thin spatula under the fish to loosen, then flip the fish over. Cook on the second side until the fish is just cooked through, about 3 minutes.

Step 5

Transfer the fish to a plate skin-side up and loosely tent with aluminum foil to keep warm. Wipe out the fishy oil in the pan with a paper towel.

Step 6

Heat the remaining 1 tablespoon olive oil in the same pan over medium heat until shimmering. Add the shallots and cook, stirring frequently, until tender, about 2 minutes. Add the garlic and sauté until fragrant, about 30 seconds.

Step 7

Add 2 1/4 cups low-sodium chicken broth, 1 cup milk, the remaining 1/2 teaspoon kosher salt, and 1 pinch red pepper flakes. Increase the heat to high and bring to a boil, scraping up any browned bits on the bottom of the pan with a wooden spoon.

Step 8

Break 8 ounces angel hair pasta in half with your hands and add it to the pan. Reduce the heat to medium low. Simmer uncovered, stirring and pressing the pasta down with a spatula to submerge it in liquid occasionally, until the pasta is tender and most of the liquid is absorbed (add more broth if needed), 7 to 8 minutes. Meanwhile, finely grate 1/2 ounce Parmesan cheese if needed (about 1/4 cup).

Step 9

Remove the pan from the heat. Add the parsley and lemon mixture and toss with tongs to combine. Sprinkle with the Parmesan and toss to combine. Taste and season with more kosher salt and black pepper as needed.

Step 10

Remove the skin from the fish and discard. Divide the pasta among 4 pasta bowls or plates and top with the fish browned side up. Serve with the lemon wedges.