Heat 2 tablespoons of the olive oil in a large skillet over medium-high heat until shimmering.
Add fresh spinach and cook, stirring occasionally, until wilted, about 3 to 4 minutes.
Transfer spinach to a colander and press with a large spoon to release excess liquid. Wipe out the skillet with a paper towel.
Pat chicken breasts dry with paper towels and then season with Kosher salt and black pepper.
Heat the remaining 1 tablespoon of olive oil in the skillet over medium-high heat.
Add the chicken and cook until browned, about 4 to 5 minutes per side.
Transfer the chicken to a clean platter or plate.
To the same skillet, add the shallot and cook for about 2 minutes, or until soft. If the pan is dry, add a little more olive oil. Add the garlic and sauté for another 30 seconds.
Stir in chicken stock and heavy cream, scraping up any browned bits, and bring to a boil, then reduce heat to medium-low.
Meanwhile, transfer the chicken to a cutting board and cut it into strips or bite-sized pieces. Add back into the sauce and simmer for 15 to 20 minutes, or until the sauce has reduced by about 1 cup.
Off heat, stir in the cooked spinach, ½ cup Parmesan, lemon zest, fresh lemon juice, ½ teaspoon salt, ½ teaspoon pepper, and the red pepper flakes.
Adjust oven rack to upper-middle position and heat broiler to HIGH. Sprinkle the remaining ¼ cup Parmesan over the top of the chicken florentine.
Broil until golden brown, about 3 to 5 minutes, or less (keep a close eye, broilers vary!). Serve at once over cooked pasta or steamed rice.