In a saucepan, simmer apricots, 1/3 cup wine, the orange zest, and 2 tbsp. honey over low heat, uncovered, stirring occasionally, until apricots are soft and liquid is absorbed, 10 to 25 minutes.
Meanwhile, preheat oven to 350°. Put hazelnuts and almonds in 2 separate shallow 9-in. pans. Bake until nuts are golden, shaking occasionally, about 10 minutes. Pour hazelnuts into a towel and rub to remove as much skin as possible; discard skin.
In a bowl, whisk eggs, remaining wine and honey, vanilla, and butter until blended. Stir in nuts.
Press pastry over bottom and up side of a 10- to 11-in. tart pan with removable rim. Distribute apricots evenly over pastry. Pour nut mixture over fruit, arranging evenly.
Bake tart on bottom rack of oven until golden brown, 50 to 55 minutes. Cool in pan on a rack, then remove pan rim. Serve dolloped with whipped cream if you like.
Make ahead: Cover and chill up to 1 day.
Note: Nutritional analysis is per serving.