Step 1

In the bowl of a food processor, combine the flour, sugar, and salt; pulse a few times to blend. Add the butter and pulse until the mixture resembles coarse meal. Add 3 tablespoons water and pulse just until the mixture is moistened and holds together when gently squeezed. Add up to 1 more tablespoon water if necessary but be careful not to make the dough too wet. Tip the dough out onto a piece of plastic wrap. Use the edges of the plastic wrap to lift and press the dough into a cohesive piece. Wrap with plastic and shape into a flat rectangle. Chill for at least 1 hour (and up to 3 days).

Step 2

In a small pot, combine the milk and cardamom; bring to a simmer over medium-high. Turn the heat off and let stand, covered, for at least 30 minutes (or up to an hour).

Step 3

Place the bittersweet and milk chocolate in a medium bowl and place a fine-mesh sieve on top. In a small bowl, whisk together the cornstarch and sugar.

Step 4

Whisk the cornstarch mixture into the pot of milk. Whisk in the cream, egg yolks, butter, and salt until thoroughly blended. Bring the mixture to a simmer over medium heat, stirring constantly, until it has come to a very slow boil for 1 minute and has thickened nicely. You may have to switch between a whisk and a spatula to ensure a smooth texture. Adjust the heat as necessary to keep the mixture from scalding or overheating. Immediately pour the custard through the sieve over the chocolate, using a rubber spatula to push the custard through the sieve. Discard the solids in the sieve. Whisk the hot custard into the chocolate until the custard is smooth. Top with a piece of plastic wrap and let cool.

Step 5

Meanwhile, heat the oven to 375°F. Roll the dough into a 12-inch circle. Fit into a 9-inch fluted tart pan with a removable bottom. Run a rolling pin over the top of the tart pan to trim the edges neatly. Freeze for 10 minutes.

Step 6

Set the chilled tart pan on a rimmed baking sheet. Line the dough with parchment and fill with pie weights; bake until the crust has set, about 20 minutes. Remove the parchment and weights and continue to bake until the crust has browned nicely, 10 to 12 minutes more. Transfer to a rack to cool completely.

Step 7

Once the tart shell has cooled, pour in the chocolate custard and smooth top. Cover with plastic wrap and chill for at least 1 hour and up to overnight

Step 8

While the tart chills, prepare the pistachio-sesame brittle: Line a rimmed baking sheet with a silicone baking mat or parchment. Place 2 tablespoons of water in a small saucepan. Add the granulated sugar and salt to the center of the pan. Bring the mixture to a simmer over medium heat, carefully swirling the pan, until it is golden amber color, 6 to 8 minutes. Immediately remove the pan from the heat and stir in the pistachios and sesame seeds. Tip out the mixture onto the prepared baking sheet and press it into an even layer with a rubber spatula. Let cool completely, then finely chop.

Step 9

To serve, whip the cream with the confectioners’ sugar and cardamom to soft peaks. Top the tart with the cream. Sprinkle the brittle over the top. Cut into wedges and serve immediately.