Preheat the oven to 350 degrees . In a bowl, toss the dried fruit with the liqueur. In a large bowl, whisk the flour, sugar, zest, cinnamon, baking powder, baking soda, salt, allspice and cloves.
In a medium bowl, whisk the eggs. For the egg wash, transfer 1 tbsp. whisked egg to a small bowl and whisk in 1 tbsp. water. Whisk the butter and vanilla into the remaining eggs in the medium bowl; add to the flour mixture. Using an electric mixer, beat at low speed, occasionally scraping down the bowl, until just blended. Stir in the fruit mixture and pistachios.
Divide the dough in half; form each half into a 12-inch loaf. Place the loaves 3 inches apart on a parchment-lined baking sheet. Brush the loaves with the egg wash and bake until the tops are golden brown, 25 to 30 minutes. Transfer the loaves to a rack; let cool 30 minutes.
Cut each loaf crosswise into 1/2-inch-thick slices. Stand slices, rounded side up, 1 inch apart on the same parchment-lined baking sheet. Bake the biscotti until lightly browned, 20 to 25 minutes. Transfer the biscotti, on the parchment, to a rack; let cool completely.
Place three-quarters of the chocolate in a small microwavable bowl. Microwave on high in 15-second increments, stirring in between, until the chocolate is melted. Add the remaining chocolate; stir until smooth. Dip the biscotti into or drizzle with the chocolate; place on a parchment-lined baking sheet. Refrigerate until set, 30 minutes.