Prepare the pasta water: Bring a large pot of water to a boil over high heat. Add the 2 teaspoons salt once the water is boiling.

Season the chicken: Pat the chicken pieces dry with paper towels. Season them evenly with the salt, black pepper, smoked paprika, and garlic powder.

Cook the linguine: Add the linguine to the boiling water and cook according to the package directions until just al dente. Before draining, reserve 1 cup of the pasta cooking water. Drain the linguine without rinsing it.

Sear the chicken: While the pasta cooks, heat the olive oil and 1 tablespoon of the butter in a 12-inch skillet over medium-high heat. Add the chicken in a single layer. Cook for 6 to 8 minutes, turning occasionally, until browned and the thickest pieces reach 165°F (74°C). Work in two batches if necessary to avoid crowding.

Rest the chicken: Transfer the cooked chicken to a clean plate and loosely cover it. Leave any browned bits in the skillet because they will add flavor to the sauce.

Bloom the aromatics: Reduce the heat to medium: Add 2 tablespoons of the remaining butter, followed by the garlic, red pepper flakes, and smoked paprika. Cook for about 30 seconds, stirring constantly, until fragrant. Do not allow the garlic to brown.

Build the sauce: Pour in the chicken broth and scrape the bottom of the skillet to release the browned bits. Whisk in the heavy cream, Dijon mustard, Worcestershire sauce, and lemon zest. Bring the mixture to a gentle simmer.

Reduce the sauce: Simmer for 3 to 4 minutes, stirring occasionally, until the sauce thickens slightly. It should coat the back of a spoon but still look loose enough to toss with pasta.

Add the Parmesan: Reduce the heat to low: Add the 3/4 cup Parmesan in small handfuls, whisking until each addition melts. If the sauce looks grainy, remove the skillet from the heat and whisk in 1 tablespoon of reserved pasta water.

Finish the cowboy butter sauce: Add the remaining 3 tablespoons butter one piece at a time, whisking until smooth. Stir in the lemon juice, parsley, and chives. The sauce should look glossy, creamy, and evenly speckled with herbs.

Combine the pasta and chicken: Add the drained linguine and cooked chicken, along with any juices from the plate. Toss over low heat for 1 to 2 minutes until everything is coated and hot. Add reserved pasta water 2 tablespoons at a time if the sauce is too thick.

Rest and serve: Remove the skillet from the heat and let the pasta rest for 5 minutes. Toss once more before serving, adding another splash of pasta water if needed. Garnish with additional Parmesan and serve with lemon wedges, if using.