How to Make It
Preheat oven to 300°F. Lightly coat a 9-inch tart pan with cooking spray. Place 1 3/4 cups of the pistachios on a rimmed baking sheet. Bake until lightly toasted, about 8 minutes. Remove from oven, and let cool 15 minutes. Increase oven temperature to 350°F. Process toasted pistachios in a food processor until finely ground and beginning to clump together, about 1 minute. Place ground pistachios and fine sea salt in a medium bowl; set aside.
Beat egg whites on high speed until stiff peaks form. Fold egg whites into ground pistachios. Press pistachio mixture into bottom and up sides of tart pan. Place tart pan on a baking sheet. Bake at 350°F until browned, about 20 minutes. Let cool completely, about 30 minutes.
Spread apricot preserves in an even layer in crust. Bring half-and-half just to a boil in a small saucepan over mediumlow. Pour hot half-and-half over chocolate in a medium bowl; let stand 1 minute. Stir chocolate mixture until smooth, pour over apricot preserves. Chill tart until chocolate is set, about 2 hours. Chop remaining 2 tablespoons pistachios. Sprinkle chopped pistachios and flaky sea salt over top of tart.