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Bring a large pot of water to a boil. Add pasta and cook until just tender, about 4 minutes. Reserve 1/4 cup of the pasta water, then drain and keep the pasta warm.
Meanwhile, cut chicken into 1-inch cubes and sprinkle with 1/4 teaspoon each salt and pepper. Place flour in a shallow dish. Add chicken and toss to coat.
Heat 1 tablespoon oil in a large cast-iron skillet or flat-bottom carbon-steel wok over medium-high heat until shimmering. Add the chicken and cook, stirring, until browned and just cooked through, 4 to 5 minutes. Transfer to a plate.
Add the remaining 2 tablespoons oil, fennel and garlic to the pan; cook, stirring, until the vegetables just start to soften, 1 to 2 minutes. Add tomatoes, snap peas, wine, the reserved pasta water and the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Continue to cook, stirring, until the tomatoes start to burst, about 3 minutes.
Return the chicken to the pan along with tarragon; cook, stirring, until the liquid is slightly thickened, about 2 minutes more. Serve the chicken and vegetables over the pasta.