Combine sugar and milk in a saucepan and bring to a boil over medium-high heat, stirring occasionally. Boil mixture for 3 minutes, then turn off the heat and pour into a bowl. Let cool to room temperature, about 30 minutes.

Add pistachio butter, almond extract, vanilla extract, and green food coloring. Whisk together, then refrigerate until completely chilled, about 2 hours.

Pour very cold whipping cream into a large mixing bowl, and whisk until soft peaks form. Transfer in half the pistachio mixture, and mix briefly to combine. Add remaining pistachio mixture and mix just until combined.

Use a spatula to transfer the mixture into a frozen container. Sprinkle half the nuts and chocolate chips over the top, and stir gently with a fork until distributed evenly. Scatter remaining chips and nuts over the top as evenly as possible.

Place a piece of plastic wrap on top of the ice cream, cover with the lid, and transfer to a freezer until completely frozen, at least 4 hours and preferably overnight.