Filling: bring a medium pot of water to a boil; add salt and farro; cook until the farro is tender, about 20 minutes.
Drain well and set aside to cool.
Combine the cooled farro, dried cherries, raisins, Marsala, and cinnamon in a bowl; let stand at room temperature for 1 hour.
Dough: combine the butter and powdered sugar in a bowl of an electric mixer fitted with the paddle attachment and mix on medium speed, scraping down the sides of the bowl once or twice, until well combined, about 2 minutes.
Add the flour and mix on low speed until combined.
Turn the mixer to med-high speed and beat until the dough is soft and smooth, about 6 minutes.
Form the dough into a ball, wrap in plastic, and refrigerate for 20 minutes.
Preheat the oven to 375°; butter the bottoms and sides of a 10-inch springform pan.
Wrap the outside of the pan with 2 squares of heavy-duty foil.
On a lightly floured surface, roll out the dough into an 11-inch circle.
Transfer it to the prepared pan and pat it firmly into the bottom and up the sides of the pan.
Place the pan in the freezer for 5 minutes to allow the dough to firm up.
Cut a 12-inch circle of parchment and place it on top of the dough; to weigh it down, cover the paper with 2 cups dried beans.
Bake the crust for 7 minutes.
Remove the beans and parchment, and bake until the crust is dry and golden brown, about 12 minutes.
While the crust is baking, combine the ricotta, cream cheese, and mascarpone in a clean mixer bowl and mix on low with the paddle attachment, scraping down the sides of the bowl once or twice, until well combined.
Add the sugar and mix for 2 minutes; add the eggs, vanilla, lemon zest, and heavy cream, turn the mixer to med and mix for another 2 minutes.
Bring about 4 quarts of water to a boil in a pot or large kettle.
Remove the springform pan from the oven and place it in a roasting pan; lower the oven temperature to 275°.
Spread half the cheese mixture evenly into the crust; spread half of the fruit mixture over the cheese and drizzle the liquid from the bowl over the fruit.
Spread the remaining cheese mixture evenly over the fruit, and sprinkle with the remaining fruit.
Place the roasting pan in the oven and pour enough boiling water into the roasting pan to came about halfway up the sides of the springform pan.
Bake for 15 minutes; increase oven temperature to 300° and bake for another 15 minutes.
Increase heat to 325° and bake until the cake is set around the edges but a little loose in the middle, about 30 minutes.
Remove the springform pan from the water bath; carefully remove and discard the foil, and set the pan on a wire rack.
Run a sharp paring knife around the inside of the pan to loosen the sides of the cake, and let cool to room temperature before removing the cake from the pan, slicing, and serving.
The cheesecake is best served on the day it is made.