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In a medium bowl, combine the water with the yeast and 1 teaspoon of the flour and let stand until dissolved. Add the sugar and a pinch of salt and stir in enough of the flour to form a stiff dough. Scrape the dough onto a lightly floured work surface and knead until smooth. Put the dough in a lightly oiled bowl, cover and let rise in a warm, draft-free place until doubled in bulk, 1 to 1 1/2 hours.
Light a grill; lightly brush the grate with oil. Deflate the dough and form it into 4 balls. On a floured surface, roll each ball out to a 7-inch round. Brush lightly with olive oil. Transfer the rounds to the grill and cook over a moderate fire for 2 minutes, or until the bottoms are browned and crisp. Flip the rounds and sprinkle the Gorgonzola and soppressata on top. Grill just until the cheese is melted and the bottoms are golden; move the pizzas as necessary to avoid burning. Transfer the pizzas to plates and top with the grapes and chives. Serve immediately.