Heat the oil in a medium saute pan over medium heat. Add the tomatoes, garlic and shallots and cook, stirring occasionally, until softened and juicy, but with no color, about 5 minutes.
Transfer the mixture to a blender, add a few tablespoons olive oil, the parsley, vinegar, honey, oregano and red pepper flakes and blend until slightly chunky; season with salt and pepper. If too thick, pulse in a bit more olive oil. Transfer the sauce to a bowl. (Can be made 1 hour before and kept at room temperature.)
Preheat the grill for high direct heat.
Remove the top shells of the oysters. Loosen the oysters from the bottom shells but do not remove, taking care not to spill the liquor. Put the oysters on the grill, cover and cook just until the edges start to curl, about 1 minute.
Meanwhile, wet the kosher salt with water just until it clumps together. Spoon little mounds of salt onto a large platter. Place a cooked oyster on each salt bed and top each with some vinaigrette. Scatter the parsley leaves over the platter and serve.