Boil the pasta
Fill a large pot with water, season it generously with salt, and bring it to a boil over high heat. Add the pasta and cook until al dente according to the package directions, stirring once or twice so it does not stick. Before you drain it, scoop out about 1/2 cup of the pasta water and set that aside for later, then drain the pasta.
Butterfly the chicken
Set the boneless skinless chicken breasts on a cutting board and, using a sharp knife, carefully slice each one horizontally to make thinner cutlets. If any pieces are especially thick, gently open them like a book so they cook evenly. Pat the chicken dry with paper towels so it will brown instead of steam in the pan.
Season and coat
Season both sides of the chicken with black pepper and a little more salt. Sprinkle on a light dusting of all-purpose flour, then shake off any excess so the coating stays thin and delicate rather than pasty.
Sear the chicken
Heat 1 to 2 tablespoons of olive oil in a large skillet over medium heat. When the oil looks fluid and shimmery, lay in the chicken without crowding the pan. Sear until the first side is deeply golden, about 3 to 4 minutes, then flip and cook the second side for 3 to 4 minutes more. Transfer the chicken to a plate and loosely cover it with foil.
Cook the aromatics
Lower the heat to medium-low. If the skillet looks dry, add another small splash of olive oil. Stir in the garlic and cook for about 30 seconds, just until fragrant. Add the tomato paste and cook, stirring, for 45 to 60 seconds until it darkens slightly and smells richer. Sprinkle in the dried oregano and red pepper flakes, then stir everything together so the spices bloom in the fat.
Deglaze the pan
Raise the heat to medium-high and pour in the chicken stock. Scrape the bottom of the skillet with a wooden spoon to loosen all the browned bits left from the chicken. Let the liquid bubble and reduce by about half, 2 to 3 minutes, so the flavor concentrates before you add anything creamy.
Build the sauce
Lower the heat to medium-low and stir in the coconut milk until the sauce is smooth and creamy. Add the sun-dried tomatoes, then stir in half of the spinach. Cook for 1 to 2 minutes, stirring gently, until that first batch of spinach wilts into the sauce. Taste the sauce and adjust with a little more salt or black pepper if it needs it.
Finish the chicken
Return the chicken and any juices from the plate to the skillet, nestling the pieces into the sauce. Let it simmer gently for 4 to 6 minutes, until the chicken is fully cooked and reaches 165° F in the thickest part. Stir in the remaining spinach and cook just until wilted. If the sauce has thickened more than you want, loosen it with a splash of the reserved pasta water until it turns silky and spoonable.
Serve and garnish
Divide the pasta among bowls or plates, then spoon the chicken and creamy tomato-spinach sauce over the top. Finish with torn basil and an extra grind of black pepper if you like. Serve right away while the sauce is hot and glossy.
