Heat 2.0 tsp oil in a 12-inch skillet over medium heat until shimmering.

Add the 12.0 oz (340.2 g) of spinach, a handful at a time, and cook, stirring often, until wilted, about 5.0 minutes.

Transfer spinach to a colander and press with a rubber spatula to remove excess liquid. Alternatively, use thawed frozen spinach, pressed dry.

Pat the chicken dry with paper towels and season with sea salt and pepper. Wipe out the now-empty skillet with paper towels, add the remaining 2.0 tsp oil, and heat over medium-high heat until very hot. Brown lightly on both sides, 4. 0 to 6.0 minutes total; transfer to a plate.

Add the minced shallot and garlic to the oil left in the skillet and cook over medium heat until fragrant, about 0.5 minutes (30 seconds).

Add the 2.0 cups of broth and 1.0 cup of the water, scraping up any browned bits.

Add the browned chicken and any accumulated juices and bring to a simmer.

Reduce heat to medium-low and cook until chicken registers 160°F (71°C), about 10.0 minutes.

Transfer chicken to a carving board and tent loosely with aluminum foil.

Meanwhile, continue to simmer the sauce until slightly thickened and reduced to 0.75 cups, about 15.0 minutes.

Whisk the 1.0 tbsp tapioca flour into the remaining 0.25 cups water in a small bowl and set aside.

Remove skillet from heat, whisk in the 2.0 tbsp coconut milk, 1.0 tsp lemon zest, and 1.0 tsp lemon juice.

Whisk in the tapioca starch and water mixture and stir until thickened.

Season with sea salt and pepper to taste.

Adjust oven rack to a position 5.0 inches from the broiler element and heat the broiler.

Slice chicken crosswise into 0. 5-inch thick slices and arrange slices in a 2. 0-quart, broiler-safe baking dish. Scatter the spinach over the top, then cover with the sauce and sprinkle with the 2.0 tbsp cheese. Broil until the cheese is spotty brown, about 0. 5 to 1.5 minutes. Allow to cool slightly before serving.

Squeeze That Spinach: This is the most crucial step! Spinach holds a ton of water. If you don't squeeze it really dry after wilting (or thawing), your creamy sauce will turn into a watery soup.

Don't be shy—use the back of a spoon or even your hands (once it's cool enough) to get all that liquid out.

Don't Skip the Slurry: When adding the tapioca or arrowroot starch, make sure you mix it with cold water first to create a "slurry" before adding it to the hot pan. If you dump dry starch directly into hot liquid, it will clump up immediately and give you a lumpy sauce.

Watch the Broiler Like a Hawk: Broilers are notoriously unpredictable. The difference between "perfectly golden" and "burnt crisp" can be a matter of 15 seconds.

Don't walk away from the oven during that final step; keep an eye on the cheese until it's just right.

The "Tent" Trick: After you cook the chicken in the skillet, letting it rest under a "tent" of foil is essential. This allows the juices to redistribute throughout the meat, ensuring your chicken is juicy and tender when you slice it, rather than dry and tough.

Zest First, Juice Second: It is infinitely easier to zest a whole lemon than one that has already been cut and squeezed. Always grab your zester before you reach for the knife!