Fill a large 4- to 6-quart container with 6 cups cold water and whisk in 2 tablespoons of the kosher salt to dissolve. Add the marrow bones, cut-side down, and top with the ice. Refrigerate for 24 hours.
When ready to cook, heat the oven to 425°F and place a rack in the center position.
Drain the bones and pat dry with paper towels. You want the bones to cook as level as possible to minimize the loss of fat as it renders out, so place them cut-side down on a small sheet pan. Cover with a generous layer of aluminum foil, then use your hands to mold the foil around the bones and sides of the pans. Place a second pan on top of the foil, then flip the whole apparatus over. Remove the sheet pan that is now on top to reveal the bones, cut-side up, and nestled in foil. They should be pretty close to dead level.
Roast the bones for 8 minutes, then rotate the pan and continue roasting until the bones have browned and the marrow is spreadable and soft, but not melted, 15 to 18 minutes total.
While the bones roast, make the parsley topping. Whisk the oil, lemon juice, and a pinch of salt together in a medium bowl. Add the parsley leaves, celery leaves, celery stalk, garlic, lemon peel, shallot, and capers, and toss to combine.
When the bones are finished, immediately dose about a third of the parsley mixture over the marrow and wait 5 minutes. Then, carefully transfer to a platter and serve with the toast, flaky salt, and remaining parsley mixture.