How to Make It
Prepare the crust: Pulse flour, powdered sugar, dry milk, and kosher salt in a food processor 3 to 4 times or until combined. Add 3 tablespoons butter; pulse until mixture resembles sand. Combine oil and ice-cold water in a small bowl. With processor running, slowly pour oil mixture through food chute; process until dough is moistened and beginning to clump. Transfer dough to a 9-inch glass pie plate; press evenly into bottom and up sides of pie plate. Prick dough all over with a fork. Freeze 1 hour (or up to 2 months).
Preheat oven to 350°F.
Prepare the filling: Place coffee liqueur in a medium, heavy saucepan; bring to a boil over medium heat. Boil until reduced to about 1/4 cup, 12 to 15 minutes. Add corn syrup, brown sugar, granulated sugar, and coffee granules; cook, stirring often, until sugars dissolve, about 3 minutes. Remove from heat; stir in half-and-half, chocolate-hazelnut spread, 1 tablespoon butter, and vanilla. Cool mixture to room temperature, about 20 minutes.
Lightly beat eggs and egg yolk in a small bowl; add to coffee mixture, and stir until combined. Spread hazelnuts in bottom of prepared piecrust; pour coffee mixture over nuts. Bake at 350°F until center is just set, about 40 minutes. Loosely cover pie with foil after 15 minutes to prevent overbrowning. Remove pie from oven; sprinkle evenly with flaked sea salt. Cool on a wire rack 30 minutes before serving.