Bring half of the water to a boil with the rest of the ingredients, whisking to dissolve the salt and honey.
Transfer the brine to another container big enough to hold the pork chops and add the remaining water (can be a combination of ice and water). Cool completely before adding the pork.
Place the pork chops in the brine and refrigerate for 1 to 2 hours.
Thoroughly rinse and dry the chops with paper towels. Then let the pork sit out for 15 to 30 minutes to get to room temp before cooking.
To cook the pork chops and green beans
Preheat air fryer to 375 degrees F.
Drizzle oil over the pork chops and green beans, then place on the air fryer basket. The green beans will be done in about 10 minutes and the pork chops will be done in about 20 minutes, or until the desired doneness is reached.
Rest the chops for at least 5 minutes before serving.
To make the sauce
While the pork cooks; sauté the mushrooms in a medium skillet over medium-high heat with some olive oil until they brown, stirring frequently.
Add 1 tablespoon butter, the chopped shallot, chopped garlic and cook until soft.
Add the vermouth and cook down until most of the liquid is gone.
Add the heavy cream and continue to cook until the desired sauce consistency is reached.