Adjust oven rack to upper-middle position and heat broiler. Heat 1 tablespoon oil in 12-inch skillet over medium-high heat until shimmering. Add spinach and cook, stirring occasionally until wilted, 1 to 2 minutes. Transfer spinach to colander set over bowl and press with spoon to release excess liquid. Discard liquid.

Pat chicken dry with paper towels and season with salt and pepper. Wipe out pan and heat remaining 1 tablespoon oil over medium-high heat until just smoking. Cook chicken on both sides until golden, 4 to 6 minutes. Add shallot and garlic to skillet and cook until fragrant, about 30 seconds. Stir in broth, water, and cream and bring to boil.

Reduce heat to medium-low and simmer until chicken is cooked through, about 10 minutes; transfer chicken to plate and tent with aluminum foil. Continue to simmer sauce until reduced to 1 cup about 10 minutes. Off heat, stir in 4 tablespoons Parmesan and lemon zest and juice.

Cut chicken crosswise into 1/2-inch-thick slices and arrange on broiler-safe platter. Scatter spinach over chicken and pour sauce over spinach. Sprinkle with remaining Parmesan and broil until golden brown, 3 to 5 minutes. Serve.