Choose a glass, plastic or stainless 3-cup bowl with a tightly fitted lid. Make sure it is dry, snap on the lid and place in freezer. In a medium bowl, dissolve all but 2 tablespoons of sugar into espresso and taste. It should taste too sweet; if not, gradually add some or all of remaining sugar, until it does. Add water, stir and pour into a stainless-steel pan or glass dish so liquid forms a pool about 1 inch deep. Cover and freeze about 1 to 2 hours until espresso has a very thick crust, but has not quite frozen through. Place pan on a cool surface in a cool room. Use a stainless steel pastry scraper (their relatively dull edges tease frozen crystals apart without slicing them up. A knife blade produces a finer, denser texture) to cut through and lift the layer of coarse crystal-ice, amalgamating it with the unfrozen core. A few cuts and folds are usually sufficient. Cover pan and return to freezer. Check hourly and when it is firm to the touch but still yields easily to a stab with pastry scraper (due to high concentration of sugar, this may take up to 8 hours), it is ready for final chopping.
Set pan of frozen espresso on a cool surface and methodically chop the crystalline blocks into a regular flaky, granular mass. This can be tedious, but it is easy, as long as you haven't let the liquid freeze too solid. If it is rock hard, it will take more brawn to cut through chunks and you may overwork some bits as you try to split harder pebbles. At opposite extreme, in rare instances where mixture is fairly sweet or thick, it may never fully freeze hard and will chop to a rich, grainy-slushy texture. Such "defective" granitas can be exquisite. Transfer granita to chilled container, snap on lid and place in freezer.
Ten to 15 minutes before serving, turn container upside down in freezer (espresso syrup sometimes drains from ice crystals, like syrup in a snow cone; turning it upside down will redistribute the syrup). Place 5-to 6-ounce bowls or glasses in freezer to chill. I use clear, narrow, fluted stemware to show off the layers and crystals.
Take the cold, medium-size bowl from the freezer, combine cream and sugar and whip until stiff. To serve, layer granita and whipped cream like a parfait in chilled glasses. There should be nearly as much whipped cream as granita. The cream's surface will freeze where it touches the granita, and the succession of voluptuous chewy and slushy textures is delightful.