One 10-inch springform or layer pan, buttered and the bottom lined with a disk of parchment or waxed paper, or 12 4-inch individual pans, buttered. Set a rack at the middle level of the oven and preheat to 350 degrees. Place the hazelnuts and 3/4 cup of the sugar in a food processor and pulse until the mixture is finely ground. Transfer to a bowl and stir in the flour. Melt the butter in a medium saucepan over medium heat. Continue cooking the butter until it colors slightly, swirling the pan to color it evenly. Remove from heat and add the rum and vanilla extract. Set aside to cool slightly. In a clean, dry bowl, whip the egg whites with the salt until they form a very soft peak. Add the remaining 3/4 cup sugar in a very slow stream, whipping constantly. Continue whipping the egg whites until they hold a soft peak. Alternately fold the hazelnut and butter mixtures into the egg whites, 1/3 at a time. Begin with the hazelnut mixture and end with the butter. Pour the batter into the prepared pan or pans. Smooth the top and sprinkle with the sliced or chopped hazelnuts. Bake the financier for about 50 minutes until well risen and golden, about 30 minutes for the individual cakes. The center of the cake should feel firm when pressed with the palm of the hand. Cool the financier briefly on a rack and remove pan and paper. If some of the hazelnuts on the surface fall off, replace them on the cake. Dust very lightly with confectioners' sugar.
For the compote, rinse, pit and quarter plums. Combine sugar and lemon juice in a small pan and heat until sugar begins to melt. Stir occasionally until sugar turns to a deep amber caramel. Add butter and water carefully off heat to prevent splattering. Return to heat, bring to a boil and add plums. Simmer a minute or two, add cinnamon and cool. To serve, place a financier off center on a plate and spoon plum compote next to it. Top with Creme Fraiche.