Bring a large pot of water to a boil, add a generous pinch of salt, and cook pasta to just shy of al dente, according to package directions. Drain and set aside.
While pasta cooks, lightly sprinkle the chicken on both sides with salt, pepper, garlic powder, and lemon zest.
In a large skillet over medium-high heat, add 1 Tablespoon each of olive oil and butter. When the pan is hot and the butter just melted, cook the chicken for 3-4 minutes per side, until golden brown and very nearly cooked through. Remove to a plate and set aside.
Reduce heat to medium, and add the remaining 1 Tablespoon each of olive oil and butter to the pan. Add garlic and red pepper flakes. Cook 30-60 seconds, just until fragrant.
Pour in white wine and, as it bubbles, scrape the browned bits from the bottom of the pan to incorporate them into the sauce. Add broth, lemon juice, a bit more lemon zest, and Italian seasoning, then bring the sauce to a simmer. Let it bubble for about 1 minute.
Add drained pasta and Parmesan. Toss well, sample, and add more salt and black or red pepper to taste.
Nestle chicken breasts back into the skillet among the pasta. Let cook for another 1-2 minutes, just until chicken is fully cooked through. Garnish with lemon wedges and fresh parsley or thyme, plus an extra sprinkling of Parmesan as desired. Serve right away.
Notes
Adjust the red pepper flakes to your taste: With just the suggested 1/4 teaspoon in the sauce, the overall dish is still pretty mild, but if your family is super sensitive to heat, consider cutting it back to 1/8 teaspoon or omitting it entirely. On the other hand, if you love a little kick, sprinkle extra red pepper flakes over everything prior to serving, or pass them at the table.
If you prefer to pre-slice the chicken, go ahead and cook it all the way through in the second step, then slice it on a cutting board and add in bite-sized pieces to the pasta.