Pat the chicken breasts dry with paper towels and dredge in a mixture of flour, salt, and pepper to coat.

Heat olive oil and butter in a large skillet over medium heat and sear the chicken for 3-4 minutes per side until golden brown.

In the same skillet, melt another tablespoon of butter and sauté chopped shallots until translucent, then add garlic and cook until fragrant.

Pour in chicken broth, scrape the skillet, and let the mixture simmer for 2-3 minutes.

Stir in heavy cream, sun-dried tomatoes, oregano, and red pepper flakes, then simmer for 5-7 minutes until thickened.

Add grated Parmesan cheese and stir until melted, adjust seasoning if needed.

Return chicken to the skillet and let it simmer in the sauce for 2 minutes, adding fresh basil before serving.

Cook pasta according to package instructions, reserving some cooking water before draining.

Toss the cooked pasta with the chicken and sauce, adding reserved water for consistency, and serve garnished with extra cheese and basil.