Chop the chocolate and put in a heatproof bowl. Bring the heavy cream, butter and salt to a simmer in a saucepan over medium heat; pour over the chocolate and let sit until completely melted, about 10 minutes. Stir with a rubber spatula or whisk until smooth. (If necessary, microwave in 20-second intervals until the chocolate melts.)
Whisk in the vanilla and almond extracts and the rum. Stir until the ganache is smooth and shiny. Pour into a shallow baking dish and refrigerate until firm, at least 3 hours or overnight.
Roll tablespoonfuls of the ganache into 18 to 24 balls, then roll in crushed amaretti cookies. Transfer to a parchment-lined baking sheet, cover with plastic wrap and refrigerate until firm, at least 1 hour or overnight. (To make these in advance, roll into balls but do not coat; cover and freeze up to 2 weeks. Let sit at room temperature for 20 minutes before uncovering, then roll in coating.)