Pat chicken cutlets thoroughly dry with paper towels. Season both sides with 1/2 teaspoon sea salt, 1/2 teaspoon cracked black pepper, 1/2 teaspoon garlic powder, and 1/2 teaspoon dried Italian herb seasoning.
Heat 1 tablespoon olive oil and 1 tablespoon butter in a large deep cast iron skillet over medium-high heat until hot and shimmering. Add chicken cutlets in an even layer. Sear for 3 to 4 minutes without moving until a deep golden-brown crust forms.
Flip chicken cutlets and cook for another 2 to 3 minutes until cooked through to an internal temperature of 165°F (74°C). Immediately transfer chicken to a warm plate and tent loosely with foil.
Reduce skillet heat to medium. Add minced garlic to the remaining pan fat and sauté for 60 seconds until fragrant and golden, being careful not to let it burn.
Pour in the low-sodium chicken broth, using a wooden spatula to scrape up all the flavorful browned pan drippings from the bottom of the skillet. Stir in the heavy cream and bring to a gentle simmer for 3 minutes until slightly thickened.
Lower heat to low. Whisk in the freshly grated Parmigiano-Reggiano cheese until completely smooth, velvety, and melted. Add the fresh baby spinach and stir for 1 to 2 minutes until just wilted.
Nestle the seared chicken cutlets and any accumulated juices back into the skillet, spooning the luxurious garlic parmesan cream over the chicken. Simmer for 1 minute to warm through.
Remove from heat. Garnish generously with freshly chopped parsley, extra cracked black pepper, and shaved parmesan curls. Serve immediately with warm pasta, potatoes, or crusty artisan bread!