Make the Strawberry Syrup: Thinly slice all the strawberries and set half aside. Place remaining half in a medium saucepan with the granulated sugar, balsamic vinegar, and salt. Cook over medium heat, stirring, until the sugar dissolves. Cover and simmer for 10 minutes, stirring occasionally, until the berries release their juices and the jam thickens.

Set a fine mesh strainer over a heatproof bowl. Pour the strawberry mixture through the strainer, reserving both the syrup and the cooked strawberry jam. Stir 1/2 cup water into the syrup, then refrigerate until ready to assemble.

In a large bowl, stir together the mascarpone and vanilla bean paste. In another bowl, beat heavy cream with the powdered sugar until soft to medium peaks form, 5 to 8 minutes. Gently fold the whipped cream into the mascarpone until just combined.

Assemble the Tiramisu. Dip half the ladyfingers into the chilled strawberry syrup, one at a time for a few seconds, just long enough to coat each side. Arrange them in an even layer in a 9x9-inch baking dish, trimming as needed.

Spread half the mascarpone cream over the ladyfingers. Gently dab the reserved cooked strawberry jam, then top with half the sliced strawberries.

For the second layer, dip the remaining ladyfingers in the strawberry syrup and arrange them over the strawberries. Spread the remaining mascarpone cream on top, followed by jam and sliced strawberries. Cover and refrigerate for at least 6 hours, or overnight, until set.

Before serving, beat 1/2 cup heavy cream with 3 tablespoons powdered sugar until soft peaks form. Spread or pipe over the tiramisu, then finish with the remaining sliced strawberries. Add chopped pistachios right before serving.