Place the chicken breasts on a cutting board. If they are very thick, gently pound them to an even ½-inch thickness for quicker, more even cooking. Pat the chicken dry with paper towels, then season both sides generously with salt, black pepper, and garlic powder if using.
Spread the flour on a shallow plate. Lightly coat each seasoned chicken breast in the flour, shaking off any excess. Heat the olive oil and butter in a large skillet over medium-high heat. When the butter is melted and sizzling, add the chicken in a single layer. Cook for 4–5 minutes per side, until golden brown and cooked through (internal temperature of 165°F). Transfer the chicken to a plate and continue with the next steps.
Combine the sun-dried tomatoes, chicken broth, heavy cream, Parmesan cheese, oregano, thyme, and red pepper flakes in a small saucepan. Stir to combine, bring to a simmer over medium heat, then stir in the minced garlic. Let cook for 2–3 minutes, allowing the sauce to reduce slightly.
Return the chicken to the skillet, spooning the sauce over the top. Cook for an additional 4–5 minutes, until the chicken is nicely coated and the sauce is hot and bubbly. Serve hot.
Serve the Marry Me Chicken hot, garnished with fresh basil leaves. Serve this dish over pasta, rice, or crusty bread. Enjoy!
To make this dish even more flavorful, drizzle a dash of balsamic glaze over the top of the chicken before serving.