Cook fettuccine in a large pot of boiling salted water according to package instructions until al dente. Reserve 1/2 cup pasta cooking water, then drain and set aside.
Pat chicken cutlets dry. Season both sides evenly with Italian seasoning, garlic powder, kosher salt, and freshly cracked black pepper.
Heat 1 tablespoon butter and 2 tablespoons sun-dried tomato oil in a large cast-iron skillet over medium-high heat. Add chicken cutlets and sear for 4 to 5 minutes per side until golden brown and cooked through (165°F internal temperature). Transfer chicken to a cutting board to rest for 5 minutes, then slice into strips.
In the same skillet over medium heat, melt remaining 1 tablespoon butter. Add minced garlic and sauté for 60 seconds until fragrant. Pour in chicken broth, scraping up flavorful browned bits from the skillet bottom.
Stir in sliced sun-dried tomatoes and simmer for 2 minutes. Lower heat to medium-low and pour in heavy cream. Bring to a gentle simmer for 3 minutes until slightly thickened.
Gradually whisk in grated Parmesan cheese in small handfuls until melted and velvety smooth. Season sauce with salt and black pepper to taste.
Add baby spinach to skillet and stir gently for 1 to 2 minutes until wilted into the sauce. Add drained fettuccine, tossing to coat strands thoroughly (add a splash of reserved pasta water if desired). Top with sliced chicken, garnish with fresh basil and extra Parmesan, and serve warm.