Begin by preparing the chicken. In a shallow dish, whisk together the flour with 1/4 teaspoon of salt and 1/8 teaspoon of freshly ground black pepper. Place one chicken cutlet in the flour mixture and coat thoroughly, pressing gently to help the flour adhere. Flip and repeat on the other side, making sure every spot is evenly dusted. Shake off any excess and transfer to a plate. Continue dredging the remaining cutlets in the same manner. Discard any unused flour mixture.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Once the oil is hot and shimmering, carefully lay the chicken cutlets in a single layer. Let them sear without disturbing them for 3 to 5 minutes, or until a rich golden crust forms on the bottom. Flip each piece with tongs and cook for another 2 to 4 minutes, until the chicken is lightly browned and fully cooked through. If necessary, cook in batches to avoid crowding the skillet.

Once the chicken is done, transfer it to a clean plate and loosely cover with foil to keep warm. Leave the browned bits in the skillet for added flavor.

Lower the heat to medium and add the remaining tablespoon of olive oil. Stir in the chopped shallots and cook until softened and translucent, about 1 minute. Add the sliced mushrooms and minced garlic, then season with the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Sauté for 2 to 3 minutes, until the mushrooms are tender and fragrant.

Deglaze the skillet by pouring in the white wine. Scrape the bottom of the pan with a wooden spoon to release all the flavorful bits. Let the wine simmer until its sharp aroma mellows, about 1 minute.

Pour in the heavy cream and bring the mixture to a gentle simmer. Gradually add the baby spinach in batches, stirring frequently until all the leaves are wilted and well combined with the sauce.

Stir in the Parmesan cheese and allow it to melt completely, forming a creamy and cohesive sauce.

Return the chicken cutlets to the skillet, nestling them into the spinach and mushroom mixture. Let everything simmer together for 2 to 3 minutes, just long enough to warm the chicken through and blend the flavors. Taste and adjust seasoning with additional salt and pepper as needed.

Serve hot, spooning the creamy Florentine sauce generously over the chicken.

Refrigerate leftovers in an airtight container for up to 3 days. To reheat, warm gently on the stovetop or in the microwave, adding a splash of cream if the sauce has thickened. This dish is not recommended for freezing, as the cream sauce may separate when thawed and reheated.