In a medium saucepan set over very low heat, melt the butter and chocolate. Remove from the heat and cool completely, 5 to 10 minutes. Add the egg and mix well. Add the marshmallows and mix until completely incorporated, then add the nuts and mix, making sure everything is coated in chocolate.
Spoon about 1/2 cup of the mixture onto a sheet of parchment paper, and use the paper to roll into a log. Repeat for the remaining mixture, about 4 logs total.
Wrap the each log in foil and freeze until firm, at least 1 hour or up to overnight.
When ready to eat, cut into 6 pieces while still frozen. Place the cookies on a serving dish to thaw for 15 to 20 minutes before serving.
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