Liberally season the chicken thighs with salt and pepper. Place the thighs skin-side down in a cast-iron pan. Cover the pan with foil and place a heavy pan, such as a dutch oven, on top of the foil as a weight.
Turn heat to medium-low and cook until the skin of the chicken thighs are brown and crispy, 20-30 minutes.
Flip chicken over and cook, this time uncovered, for 10-15 minutes or until chicken registers 165° F. Remove chicken and set aside. Drain all but 1 tablespoon of grease from the pan.
Add the shallot to the pan over medium heat and stir until it is softened, 1-2 minutes. Add the sherry and scrape up all the cooked bits from the bottom of the pan. Cook until the sherry has reduced by half. Add the spinach and tomatoes and cook until just wilted, 2-3 minutes.
Add the heavy cream and reduce until golden color about 2 minutes. Turn off the heat. Whisk in the butter a couple chunks at a time and continue until all the butter had been added. Taste and season with salt and pepper.
Serve the chicken thighs with spinach, tomatoes, and sauce.