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Step 1
Place the flour, ¾ teaspoon salt, and the black pepper in a ziplock bag and shake to combine. Add the chicken to the bag; seal the bag tightly and shake to coat the chicken evenly. Set aside.
Step 2
Heat the oil in a large nonstick skillet over medium-high heat. Place the flour-dusted chicken in the pan and cook, flipping once, until the chicken is lightly golden and just cooked through, about 3 minutes total. Transfer the chicken to a plate and set aside.
Step 3
Reduce the heat to medium and add the onions to the skillet. Cook, stirring frequently, until softened and translucent, 2 to 3 minutes. Add the garlic and cook, stirring constantly, for 30 seconds more; do not brown. Add the cream, broth, sun-dried tomatoes, tomato paste, oregano, red pepper flakes, sugar, and ¼ teaspoon salt; use a wooden spoon to scrape any brown bits from the pan into the liquid. Bring the liquid to a boil, then reduce the heat to medium and gently boil, uncovered, until the sauce is thickened, about 5 minutes. Stir in the Parmigiano Reggiano (or Pecorino Romano) and basil. Add the chicken back to the pan, along with any juices that accumulated on the plate; reduce the heat to low and simmer until the chicken is warmed through and the sauce thickens a bit more, 1 to 2 minutes. Sprinkle with more fresh basil, if desired, and serve.
Step 4
Note: I use pre-cut, ready-to-cook, thin-sliced chicken breasts for this recipe. If you'd like to use regular chicken breasts, you'll need to first cut them in half horizontally to form flat fillets, then pound them until they are between ⅛ and ¼-inch thick. (It's important to cut them in half first; otherwise they'll be enormous after pounding.)