Heat the oven to 375°F with a rack in the lowest position. Mist a 9-inch springform pan with cooking spray.

Spread the hazelnuts on a rimmed baking sheet, then toast until deep golden brown, about 10 minutes. Enclose the nuts in a kitchen towel and rub vigorously to remove the skins. Set aside.

In a food processor, combine both flours, 53 grams (¼ cup) of the sugar, the baking powder and ¼ teaspoon salt. Process until combined, about 5 seconds.

Scatter the butter over the mixture and pulse until it resembles coarse sand, 10 to 12 pulses. Add the egg yolk and ½ teaspoon of the vanilla extract, then process until evenly moistened and clumping together, 20 to 30 seconds.

Transfer the dough to the prepared pan; do not wash the food processor. Press into an even layer and prick with a fork about every ½ inch. Bake until golden in the center and slightly darker at the edges, 15 to 20 minutes.

Meanwhile, in a small microwave-safe bowl, microwave the chocolate on 50 percent power, stirring every 30 seconds, until smooth and melted. Set aside.

In the food processor, pulse the hazelnuts until roughly chopped, about 8 pulses; measure out ¼ cup and set aside. Add the remaining 161 grams (¾ cup) sugar and process until it resembles wet sand and sticks to the corners of the workbowl, about 2 minutes.

Scrape the bowl. Add the egg whites, the remaining 2 teaspoons vanilla extract, the espresso powder and ¼ teaspoon salt. Process until smooth, about 10 seconds. Add the chocolate and process until incorporated, another 10 seconds, scraping the sides as needed.

Spread the hazelnut-chocolate mixture in an even layer on the crust, then sprinkle the reserved chopped nuts around the perimeter. Bake until slightly puffed and the edges begin to crack, 20 to 25 minutes.

Let cool on a wire rack until the edges pull away from the sides of the pan, about 15 minutes. Remove the pan sides. Serve warm or room temperature.