Submerge pork chops the saucepan with the brine for 20 minutes. Remove and pat dry with paper towels.
Preheat the oven to 200 degrees F.
Season the chops on both sides with kosher salt and freshly cracked pepper. Arrange the chops on a baking sheet and put in the oven. Roast the chops until an instant-read thermometer registers 90 degrees F, about 20 minutes. Meanwhile, while the chops are in the oven, in a medium-size saucepan, add the canned cherries, 3/4 of a cup of Madeira, the orange zest, ginger, agave and a pinch of salt. Bring the mixture to a boil over high heat, then lower the heat to a strong simmer and reduce the sauce by half.
Once the chops have reached 90 degrees F, remove them from the oven.
Heat a large skillet over high heat, add the grape seed oil and heat until shimmering. Add the chops, being careful not to crowd them, and cook for 4 minutes per side. They will be golden and have a hard crust. Transfer them to a serving platter and tent with aluminum foil to keep warm. In the same skillet that the chops were cooked in, add the remaining 1/4 cup of Madeira and deglaze the pan over medium-high heat. Stir in the balsamic and cherry sauce and reduce by half. Turn off the heat, add the butter and stir to combine. Pour the cherry sauce over the chops and serve.
In a large saucepan over high heat, add the water and remaining ingredients, except the ice. Stir until the salt dissolves. Remove from the heat, add the ice and stir until cool.