Place 1 pint of pistachio ice cream in the fridge for 30 minutes to soften for easier scooping and spreading
Line an 8-inch square baking pan with two 8×14-inch sheets of parchment, leaving excess on all sides to help lift the bars later. Avoid using wax paper or foil.
Scoop the softened ice cream into the pan. Use an off-set spatula to start spreading it into an even layer. Cover with a square of parchment and use the back of a measuring cup to finish smoothing it into an even layer. Freeze until firm, about 1 hour.
Finely chop thawed kataifi with a serrated knife. In a large skillet, melt butter over medium heat. Add kataifi and cook, stirring frequently, for about 8 minutes, until golden and crisp. Avoid high heat—kataifi burns easily.
Transfer kataifi to bowl and let cool for a few minutes. Stir in pistachio cream.
Remove the pan from the freezer and spread kataifi mixture evenly over the ice cream. Press gently with a spatula. Return to freezer for 30 minutes. Place second pint of ice cream in fridge to soften.
Spread the remaining softened ice cream over the kataifi layer. Cover with a square of parchment and use the back of a measuring cup to finish smoothing it into an even layer. Cover with plastic wrap, and freeze until completely firm — at least 4 hours, preferably overnight.
Place a cutting board in the freezer to chill. Once the ice cream is frozen, line the chilled board with parchment. Use parchment flaps to lift the slab out of the pan. Invert onto cutting board, peel off parchment, and cut into 9 squares using a large, sharp knife. Wipe the blade clean between slices. Return bars to freezer, wrapped in plastic if freezing for more than 1 hour.