Dissolve a tablespoon (14 g) of sea salt in a large bowl of warm water. Add the chicken and set aside to brine.

Meanwhile, heat a tablespoon of oil in a large saute pan over medium heat. Add the mushrooms and onions. Cook for about 7-10 minutes, until onions are translucent and starting to brown.

Increase heat to medium-high. Add the zucchini. Season everything with sea salt and black pepper. Stir fry for about 10 minutes, uncovered, until the zucchini is soft and a little browned. Most (if not all) of the liquid should evaporate.

Drain the veggies if any liquid remains and transfer to a large bowl. Set aside the bowl. Set aside the saute pan to use again.

Remove the chicken from the water and pat dry. Cut into bite-size pieces.

Add another tablespoon of oil to the saute pan and heat over medium-high heat. Add the chicken pieces and saute for 3-5 minutes, until browned on both sides and cooked through.

Add the chicken to the bowl with the veggies. Set aside the bowl. Set aside the saute pan to use again.

Preheat the oven to 400 degrees F (191 degrees C).

While the oven preheats, add cream and chicken broth to the same saute pan from before (it will just be at the bottom. Bring to a simmer, and simmer gently for about 5 minutes, until thick enough to barely coat the back of a spoon.

Reduce heat to low. Stir 3 oz (85 g) of shredded cheese into the pan, until melted. Add sea salt and black pepper to taste if needed.

Pour the sauce into the bowl with the chicken and veggies. Mix to combine.

Transfer the mixture to a 9x13 in (23x33 cm) glass casserole dish. Sprinkle with remaining shredded cheese.

Bake for about 10 minutes, until the cheese melts.