In a medium saucepan over medium heat, add the butter, coffee liqueur, Franjelico, sugar and salt until melted. Whisk to combine. Add the flour and using a wooden spoon, briskly stir the flour into the liquid until a dough forms. Continue to stir the dough for 1 to 2 minutes Turn off the heat and transfer the dough into the bowl of a stand mixer fitted with the paddle attachment. Mix the dough on low-medium speed and add the mascarpone. Mix to combine. Add 1 egg at a time, mixing until incorporated and increasing the speed with each addition until the dough is sticky and glossy. Pour the dough into a large (18-inch) piping bag fitted with a large star tip.
Pipe 3- to 4-inch churros into the hot oil, cutting the dough with scissors. Fry for 2 minutes until golden brown and then flip over to fry on the other side. You may need to manipulate them with a spider or slotted spoon in the hot oil so they fry evenly. Remove with a spider onto a paper towel-lined plate to drain of excess oil. Continue to fry in batches.
Put the cocoa sugar into a fine mesh sieve and dust the churros with sugar. (You can also roll the churros in the sugar, but dusting with sugar yields a more pleasant-looking sugar coating.)