The mainstay of many a medieval recipe was nuts, especially almonds, which were ground and used to a thicken sauces, or made into white almond milk. In the Strada Nuova is a large nut stand. Here you can find almonds jostling with wonderful wet walnuts, pistachios and caramel-coloured hazelnuts.
Almond milk was a staple ingredient in the medieval Venetian kitchen. It was made then more or less as it can be made now, except that my sieve is metal rather than made from horsehair! Shop-bought almond milk is fine to use as a replacement, I would go for unsweetened in both cases. This same method can be followed to make hazelnut or cashew milk.