For the dark chocolate and salted caramel ganache: In a saucepan, melt the sugar with the water over low heat, until it becomes a caramel-colored liquid, approximately 6 to 8 minutes. Add the butter and stir until it's all incorporated. Add the cream and stir until it becomes a thick and rich caramel. Add the chocolate and stir until it's melted and incorporated in the caramel. Remove from the heat. Let cool and reserve in an airtight container.
For the raspberry mango filling: Put the raspberries, mango, sugar, lemon zest, and lemon juice in a saucepan and bring to a boil, skimming the surface of the jam regularly. Simmer for about 20 minutes. Let cool. Blend the mixture to reduce to a puree. Pass through a fine sieve to remove the seeds. Reserve in an airtight container and keep refrigerated.
For the lemon cream: In a stainless steel bowl, mix the sugar, butter, eggs, lemon zest, and lemon juice together. Place the bowl over a pot of boiling water. Cook's Note: Do not let the bottom of the bowl touch the water, you do not want to scramble the eggs.
Cook for approximately 2 minutes, until the cream thickens. Remove from the heat. Pass through a fine sieve. Cover with plastic wrap so that it is directly on top of the cream (to prevent a skin from forming). Let cool and keep refrigerated.
For the doughnuts: In a food processor, sprinkle the yeast over the warm milk and stir to dissolve; let stand for 5 minutes. Add the sugar, salt, beaten eggs, vanilla, and butter. Blend thoroughly. Add the flour and then using a stand mixer with a dough hook attachment, beat until smooth. You can also knead the dough by hand for about 5 minutes. Cover the dough with plastic wrap and chill at least 4 hours or overnight.
Roll the dough out on a floured surface to 1/2-inch in thickness. Cut the dough into 1 inch-round doughnuts using a circular cookie cutter (or alternately, a can). Cover with a plastic wrap and let rest for 1 hour in a warm place. Heat oil in a deep fryer to 360 degrees F and fry the doughnuts in batches for 1 to 1 1/2 minutes, until lightly browned on both sides. Drain on a paper towel-lined baking tray.
Fit a pastry bag with a 4 mm pastry tip and insert the tip into the side of the doughnut. Gently squeeze the bag as you slowly pull the tip out of the doughnut. Using this technique, fill the pastry bag with the prepared dark chocolate and salted caramel ganache, raspberry-mango jam, and lemon cream, changing the pastry bag after filling the desired amount of doughnuts with each filling. Sprinkle the doughnuts generously with powdered sugar. Serve warm.
Cook's Note: Chilling the dough makes it easier to roll it (does not stick as much). The dough will keep in the freezer for up to 3 months.
You can also use any good quality jams to fill the donuts.