Preheat the oven to 375 degrees F.
Heat a grill with a single layer of charcoal. When the coals are hot, brush the grill with a little oil to make sure the peaches don't stick. Place the peaches, cut side down, on the grill and cook for a few minutes, until they're slightly charred.
Place the peaches in an oven-proof dish, sprinkle each half with a little vanilla sugar. Combine the rum and amaretto and drizzle 1/2 of it on the peaches. Bake the peaches for about 10 minutes, until they're very tender. Serve hot, at room temperature, or cold with crumbled amaretti cookies on top or with the cookies on the side. I like to serve them with a dollop of creme fraiche or vanilla ice cream.
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