Pat sliced chicken breast dry with paper towels. Season evenly with Italian seasoning, 3/4 tsp salt, and black pepper.
Heat 1 tbsp olive oil and 1 tbsp butter in a 12-inch deep cast iron skillet over medium-high heat. Add the chicken strips in a single layer and sear for 5 to 6 minutes, turning once, until golden-brown and cooked through (165 F). Transfer chicken to a clean plate.
In the same skillet, melt remaining 1 tbsp butter with 1 tbsp olive oil over medium heat. Add minced garlic and sun-dried tomatoes; sautu00e9 for 60 seconds until fragrant.
Pour in chicken bone broth and heavy cream, using a wooden spatula to scrape up all flavorful caramelized browned bits (fond) from the bottom of the skillet. Bring to a gentle, steady simmer.
Add the uncooked potato gnocchi directly into the bubbling liquid, gently stirring so they are submerged. Cover the skillet with a lid and cook over medium-low heat for 4 to 5 minutes, until gnocchi are tender and pillowy.
Uncover and stir in the grated Parmigiano-Reggiano, fresh lemon juice, and baby spinach. Simmer uncovered for 2 minutes, stirring continuously, until cheese melts into a velvety cream sauce and spinach wilts.
Return the seared chicken and any resting juices back to the skillet. Toss gently for 1 minute to coat every pillow of gnocchi in the rich garlic parmesan sauce.
Remove from heat. Garnish with fresh basil ribbons, extra shaved parmesan, and freshly cracked black pepper. Serve immediately hot with warm artisan sourdough bread.