Cut 1 pound boneless, skinless chicken breasts crosswise into ½-inch thick strips. Cut each strip crosswise into 1-inch wide pieces. Toss the chicken with 1 teaspoon of the kosher salt and 1 ½ teaspoons ground coriander until evenly coated.

Heat 1 tablespoon of the olive oil in a large pot or Dutch oven over medium heat until shimmering. Add the chicken and spread it into an even layer. Cook until browned on both sides and cooked through, 4 to 5 minutes per side. Transfer to a plate.

Add the remaining 1 tablespoon olive oil and 2 tablespoons minced garlic to the pot. Cook, stirring constantly, until fragrant, about 30 seconds.

Stir in 4 cups water, 2 cups half-and-half, and the remaining 1 ¼ teaspoons kosher salt. Scrape up any browned bits from the bottom of the pot. Add 1 pound dried fettuccine pasta. Increase the heat to medium-high and bring to a simmer, stirring the pasta occasionally to separate the strands, until it begins to wilt, about 5 minutes.

Reduce the heat to medium and cook, stirring occasionally, until the pasta is al dente, 10 to 15 minutes.

Turn off the heat. Add 4 ounces grated Parmesan cheese, 1 tablespoon finely grated lemon zest, and ¼ cup lemon juice. Toss with tongs until well-combined and the cheese is melted, about 1 minute.

Return the chicken and any accumulated juices on the plate to the pot. Cover and let sit until the sauce is thickened, about 5 minutes. Toss again to recombine. Taste and season with more kosher salt as needed. Serve topped with more grated Parmesan, lemon zest, and chopped fresh parsley leaves if desired.