Melt butter in a skillet over medium-low heat; cook and stir almonds in melted butter until toasted or slightly burnt, 5 to 10 minutes. Remove from heat and cool.
Mix cream, half-and-half, sugar, cocoa mix, and vanilla extract together in a bowl; transfer cream mixture to an ice cream maker. Follow manufacturer's instructions for freezing. Add almonds, chocolate chips, and cherries once ice cream is almost stiffened and continue freezing until ice cream is completely stiffened.