¼ cup water
½ cup granulated sugar, divided
¾ cup shelled, unsalted pistachios
½ teaspoon kosher salt
3 tablespoons unsalted butter at room temperature
1 large egg, lightly beaten
1 teaspoon vanilla extract
4 day-old croissants, split in half lengthwise
1. Preheat the oven to 350°. In a small saucepan set over medium-high heat, add the water and ⅓ cup of the sugar. Cook until the sugar dissolves, about 2 minutes. Turn off the heat and set aside.
2. In a food processor, combine ½ cup plus 2 tablespoons of pistachios, the salt and remaining sugar and pulse until the nuts are finely ground. Add the butter and process until combined. Add the egg and vanilla and pulse just until combined, stopping the food processor to scrape down the sides and bottom of the bowl as necessary.
3. Brush the cut side of each croissant half with some of the simple syrup mixture. Spread 2 tablespoons of the pistachio mixture on the bottom half of the croissant and cover with a top croissant half, pressing down to slightly flatten the croissants. Arrange the croissants on a parchment-paper-lined rimmed baking sheet.
4. On a cutting board, finely chop the remaining 2 tablespoons of pistachios. Brush the croissants with more simple syrup and sprinkle the chopped pistachios on top.
5. Bake the croissants until they are golden and the pistachio filling fuses the top and bottom halves together, about 25 minutes. Remove from the oven and cool 20 minutes before sprinkling with confectioners' sugar.