BEFORE YOU BEGIN: Drain the wilted spinach in a colander to rid it of excess moisture, otherwise it will water down the sauce. Can even pat the spinach dry.
Drain the wilted spinach in a colander to rid it of excess moisture, otherwise it will water down the sauce.
Place chicken between 2 sheets of plastic wrap and pound to even 1/2-inch thickness. Pat chicken dry with paper towels and season with salt and pepper; set aside.
Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add spinach and 1/8 teaspoon salt and cook, stirring occasionally, until wilted, about 2 minutes. Transfer spinach to colander set in sink and allow any excess liquid to drain off. Wipe skillet clean with paper towels.
Heat remaining 1 tablespoon oil in now-empty skillet over medium heat until just smoking. Cook until chicken is golden brown and registers 160 degrees, about 6 minutes per side. Transfer chicken to plate and tent with aluminum foil.
Add shallot and garlic to skillet and cook until fragrant, about 30 seconds. Whisk in broth and cream, scraping up any browned bits, and bring to boil. Cook until reduced to about 2/3 cup, about 7 minutes. Off heat, stir in 2 tablespoons Parmesan and lemon zest and juice.
Transfer chicken to individual plates and stir any accumulated chicken juices into sauce. Season sauce with salt and pepper to taste. Stir spinach into sauce to warm through. Top chicken with spinach and sauce and sprinkle with remaining 2 tablespoons Parmesan. Serve.