Preheat oven to 400ºF (200ºC). Loosen the oysters from the shell and set aside in a medium bowl. Arrange the rock salt in a baking dish and firmly press the shells into the salt.
In a medium sauté pan over medium heat, add the butter and allow to melt. Add the shallots and sauté until soft and translucent, about 4 minutes. Add the garlic and sauté an additional 15 seconds.
Add the spinach, parsley, onions and tarragon and stir until the greens have wilted, about 4 minutes. Stir in the lemon juice, cayenne, paprika, salt and pepper followed by the cream.
Add the oysters back into the shells. Top with a spoonful of the greens mixture followed by the breadcrumbs and Parmesan cheese.
Bake until the breadcrumbs are lightly browned, about 15 minutes. Garnish with chives and serve immediately.