Add the sweetened chestnut purée, mascarpone, salt, vanilla, and rum if using to a bowl. Beat until smooth, then loosen with 20–30ml heavy cream until the mixture is soft enough to pipe but still thick enough to hold shape. Transfer to a piping bag with a small round tip, or use a spoon if you do not need the classic piped Mont Blanc look. The chestnut cream should be smooth, thick, and pipeable. If it is too stiff, it sits like paste. If it is too loose, it melts into the whipped cream and loses the Mont Blanc identity. This target consistency sits deliberately between two failure states — the classic Mont Blanc look depends on the chestnut cream holding fine, visible strands or ribbons once piped, which requires real body without being so stiff it resists piping cleanly.

Whip the cold heavy cream with powdered sugar and vanilla until soft peaks form. Do not whip it stiff. The cream should mound softly and still look silky. Stiff whipped cream makes the drink feel heavy and dessert-like in the wrong way. Stopping at soft peaks, rather than continuing to a fully stiff whip, keeps this layer light and yielding enough to still read as part of an iced coffee — pushed further into stiff peaks, the texture shifts toward something closer to a standalone dessert topping than a component of a drink.

Add 10ml simple syrup to each glass if using. Fill each glass with ice. Pour 90ml strong chilled coffee into each glass, then add 60ml cold whole milk. Stir briefly. The base should still taste clearly like strong coffee. The milk softens it, but it should not become pale or weak like a latte. Given how much rich cream and sweet chestnut sit above this base, it genuinely needs real coffee strength to remain noticeable once the whole drink is eventually stirred together at the end.

Spoon a generous layer of soft whipped cream over each iced coffee. Keep the cream mostly on the surface. The coffee base must be cold before the cream goes on. If the coffee is warm, the whipped cream softens immediately and the chestnut topping loses shape. A properly chilled base beneath the cream is what lets that soft-whipped layer hold its own structure rather than melting on contact — any warmth from below works directly against the cream's texture.

Pipe or spoon the chestnut cream over the whipped cream. For the most classical Mont Blanc look, pipe thin strands or short ribbons over the top so it resembles a small chestnut "mountain." The topping should sit visibly on the cream, not dissolve into the coffee. The chestnut layer is the defining feature of the drink. Piping in thin strands rather than a single mounded dollop is what produces the classic Mont Blanc texture and appearance — that specific piped structure, resembling the pastry's own signature look, is part of what distinguishes this drink from a simple chestnut-flavoured whipped topping.

Serve immediately with a straw or long spoon. The drink should be stirred lightly before drinking, but the layered cream and chestnut top should be visible first. This layered presentation is genuinely fragile — the whipped cream and piped chestnut both begin softening the moment they're built, so serving without delay preserves the visual moment this drink is specifically designed around.