If needed, place chicken between sheets of plastic and, using a meat mallet or a heavy skillet, pound to an even thickness of about ¼ inch. Season each breast on both sides with Creole seasoning and refrigerate, covered, for several hours.

To make the sauce, heat olive oil in a 12-inch skillet over medium heat. Halve the onion lengthwise and peel; slice crosswise into ¼ inch slices. Add to hot skillet with garlic and hot pepper flakes and cook, stirring occasionally, until the onion is very soft, about 10 minutes; do not brown.

Make a well in the center and add the tomato paste; cook, stirring, until fragrant and slightly caramelized, about 2 minutes. Stir the pan through and add the wine; cook until half the wine has evaporated. Add the tomatoes, Italian seasoning, bay leaf, and salt and pepper; bring to a simmer, reduce the heat to medium-low, cover, and cook, stirring occasionally, until tomatoes are soft, about 20 minutes. Taste and adjust seasoning.

While the sauce simmers, bread and cook the chicken. Combine the breadcrumbs and Parmesan in a shallow bowl; combine the egg and buttermilk in another shallow bowl. Dip the chicken in the egg wash and allow excess to drain off; dredge in breadcrumbs. Heat cooking oil in a skillet over medium-high heat. When the oil shimmers, working in batches if necessary, add the chicken breasts in a single layer and cook, undisturbed, for 5-7 minutes, until browned; flip and cook until second side is browned and internal temperature reaches 160ºF, about 5 minutes. Transfer to a cutting board, tent with foil, and let rest 5-8 minutes.

Meanwhile, bring a large, well-salted pot of water to a boil. Add pasta and cook until just shy of al dente. Use tongs or a pasta rake to transfer the pasta directly to the skillet of sauce and toss to coat; sprinkle with parsley, add about ¼ cup of the pasta cooking water, and toss again. Add additional pasta water a few tablespoons at a time as needed to make a “saucy” sauce; the pasta will finish cooking in the sauce, soaking up flavor along the way. Taste and adjust seasoning.

To serve, divide sauced pasta among 4 serving bowls and garnish with green onions and Parmesan. Slice each chicken breast across the grain and arrange atop pasta; serve hot, passing hot pepper flakes and Parmesan at the table.