Step 1Heat the oven to 350 degrees.
Step 2Cut the eggplants in half lengthwise. Using a melon baller or sharp spoon, carefully scoop out the flesh, leaving thin shells; set aside. Coarsely chop the flesh.
Step 3Heat the oil in a skillet over medium heat. Add the garlic and cook until softened, then add the chopped eggplant and thyme. Cook, stirring, until the eggplant is soft, about 5 minutes. Remove from the heat and stir in the piquillos. Cool, then stir in the bread crumbs and one-half cup of the cheese. Season with salt and pepper to taste.
Step 4Divide the stuffing among the eggplant shells. Set the shells in a baking dish that's at least 3 inches deep and large enough not to crowd the stuffed shells. Top each with the remaining cheese. Carefully pour water around the eggplants to a depth of one-fourth inch or halfway up the sides of the eggplants. Cover the dish with foil.
Step 5Bake 20 minutes. Remove the foil and continue baking until the shell is very tender, about 15 minutes longer. Serve warm or at room temperature (if not serving immediately, remove from the baking dish with a slotted spatula before cooling).