Make the coffee soak: brew 1 cup strong coffee, stir in 1 tablespoon sugar while still warm, then set aside to cool to room temperature.
Toast and chop the pistachios: warm a dry skillet over medium heat and toast the shelled pistachios, stirring, until fragrant (2–3 minutes). Let cool, then chop finely. Reserve about 1/4 cup for garnish.
Whip the cream: in a chilled bowl, beat the heavy cream to soft peaks. Cover and refrigerate briefly while you prepare the custard base.
Cook the yolks (zabaglione-style): set a heatproof bowl over a pan of simmering water (double boiler). Whisk the egg yolks with 2 tablespoons sugar until combined. Place the bowl over the simmering water and whisk continuously until the mixture becomes pale and thick enough to coat the back of a spoon, about 6–8 minutes. Remove from heat and stir in the vanilla.
Finish the pistachio mascarpone filling: while the yolk mixture is still slightly warm, fold in the mascarpone until smooth, then whisk in the pistachio paste until evenly distributed. Allow the mixture to cool to room temperature, then gently fold the whipped cream into the mascarpone mixture in two additions, keeping the mixture light and airy.
Assemble the tiramisu — first layer: quickly dip each ladyfinger into the cooled coffee (1 second per side—don’t let them soak) and arrange a single layer in a 9x13-inch (or similar) baking dish. Spread half of the pistachio mascarpone over the ladyfingers and smooth gently.
Second layer and topping: repeat with another coffee-dipped layer of ladyfingers. Spread the remaining cream evenly over the top. Press a handful of chopped toasted pistachios into the middle layer as you build it for extra texture, and scatter the reserved pistachios over the surface as garnish.
Chill and serve: cover the dish and refrigerate at least 6 hours (overnight is best) so the flavors meld and the texture sets. Cut into 8 portions and serve chilled.