In a small bowl, combine the 1 tablespoon olive oil, 1 teaspoon smoked paprika, ½ teaspoon cayenne, ½ teaspoon salt, and ½ teaspoon black pepper. If your chicken breasts are too thick, butterfly each of them through the middle to make even pieces, then coat them in the spicy marinade.
Heat a large pan over medium high heat and cook the chicken for 3 to 4 minutes per side, until lightly charred and cooked through. Set it aside to rest, then slice into thin strips against the grain.
Bring a large pot of salted water to a boil and cook the 12 ounces linguine until al dente. Reserve a cup of the pasta water before draining.
Meanwhile, turn the heat to medium and melt the 2 tablespoons butter in the same pan, scraping up the browned bits. Add the diced onion and cook until softened and lightly golden. Stir in the 3 cloves minced garlic, ½ teaspoon red pepper flakes, and ½ cup sun dried tomatoes and cook for 1 minute more.
Pour in the ⅓ cup white wine and let it reduce completely, about 3 to 4 minutes. This burns off the alcohol and leaves behind a deeper flavor, so let it cook down fully.
Add the 3 tablespoons tomato paste and fry for 2 minutes, until it darkens and sweetens. Deglaze with the ⅔ cup chicken broth, then pour in the 1¼ cups heavy cream. Bring to a gentle simmer and season with salt and pepper.
Add the 3 cups spinach and stir until wilted, about 1 minute. Use tongs to transfer the linguine straight into the pan and toss to combine.
Add the ½ cup Parmesan, 1 teaspoon lemon zest, and 2 tablespoons parsley, along with the sliced chicken and any resting juices. Toss well, adding a splash of the reserved pasta water to loosen the sauce to a silky consistency.
Serve right away, while it is hot and creamy.