In a large mixing bowl, combine the heavy cream, milk, vanilla pudding mix, and pistachio butter. Whip with a hand mixer or stand mixer on high speed until stiff peaks form. Taste and add more pistachio butter if desired.
Line a 9x9-inch/20x20 cm square baking dish with parchment paper, allowing some overhang on all sides for easy removal.
Working one at a time, dip each biscuit quickly into the cooled coffee. Arrange a single layer of dipped biscuits in the base of the prepared dish.
Spread one-third of the pistachio cream evenly over the biscuits, smoothing with an offset spatula. Repeat twice more, layering dipped biscuits and cream, ending with a final layer of cream on top. Refrigerate the assembled cake for 1 to 2 hours, until the layers are firm.
To make the ganache, combine the white chocolate, heavy cream, and pistachio butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until the chocolate is melted and the ganache is smooth. Let cool slightly.
Pour the ganache over the chilled cake, spreading it gently with a spatula. Return the cake to the refrigerator for at least 1 hour, or until fully set.
Use the parchment paper to lift the cake out of the pan. Slice into squares and serve cold. Store leftovers in an airtight container in the refrigerator for up to 3 days.