Slice the chicken breasts into 1 cm strips and season with salt. Heat the olive oil in a large skillet over high heat. Sear the chicken in a single layer until golden on both sides (not cooked through). Remove and set aside.
In the same skillet, melt the butter over medium heat. Add the onion and garlic and cook until the onion is translucent.
Sprinkle in the flour, stir to coat, and cook for about 1½ minutes. Pour in the chicken stock and heavy cream, stirring until smooth.
Add the sun-dried tomatoes, cayenne, and oregano. Stir in the grated parmesan and chopped basil until the sauce is smooth and glossy.
Meanwhile, cook the pasta in well-salted boiling water until al dente. Drain, reserving a splash of pasta water.
Return the chicken to the skillet and simmer in the sauce over medium heat for 10-15 minutes, until cooked through. Add the drained pasta and toss to coat, loosening with reserved pasta water if needed. Finish with extra parmesan and basil.