1. MAKE THE SHORTCAKES: Preheat the oven to 375°. Lightly butter a large baking sheet. On a work surface, gently fluff and separate the strands of the kataifi. Sprinkle with half of the butter and the sugar and cinnamon and toss gently to coat. Cover loosely with plastic wrap while continuing to work.
2. Using a 3-inch ring mold or a large biscuit cutter, shape 1/3 cup of the kataifi into a 3-inch round on the baking sheet. Dip a pastry brush into the remaining butter and tamp down the dough; remove the ring mold. Repeat with the remaining kataifi and butter to make 12 rounds, spacing them evenly on the baking sheet. Bake for about 15 minutes, or until golden.
3.MAKE THE FILLING: In a saucepan, combine the water with 3 tablespoons of the granulated sugar and the lime juice and bring to a boil. Cook, stirring, until the sugar dissolves.
4. Increase the oven temperature to 450°. In a large bowl, toss the plums with the remaining 1 tablespoon of granulated sugar and the butter. Spread the plums in a roasting pan and roast for about 15 minutes, or until caramelized.
5. In a medium bowl, combine the ricotta with the 2 tablespoons of confectioners' sugar and 2 tablespoons of the lime syrup. Whip the cream until it holds stiff peaks. Fold into the ricotta.
6. Set 6 of the kataifi rounds on 6 dessert plates. Top with all but 6 of the plum wedges, most of the ricotta cream, and then the remaining 6 kataifi rounds. Garnish each shortcake with a dollop of the remaining ricotta cream and a plum wedge. Drizzle with the remaining lime syrup and dust with confectioners' sugar. Serve immediately.
Make Ahead: The recipe can be prepared through Step 3 up to 1 day ahead. Store the kataifi rounds at room temperature in an airtight container between layers of wax paper. Refrigerate the lime syrup. Bring the syrup to room temperature before continuing.