Heat oven to 375°F. On a lightly floured counter, roll each sheet of puffed pastry to roughly a 9-inch square. Place each on a large baking sheet lined with parchment paper. Dock all over with a fork. Place another piece of parchment paper on top, then another 1 or 2 baking sheets on top of the parchment paper to weight it down. Bake in oven for 18 to 20 minutes, then remove the baking sheet weights and top sheet of paper and bake for another 5 to 10, or until golden brown. Set pastry aside to cool completely.

Line the base and sides of an 8×8-inch cake pan with a large sheet of foil so the excess goes up the sides. Place first cooled square of pastry on a cutting board and use bottom of cake pan to cut it into a square that will fit tightly inside the pan. Repeat with second square. Place first square inside the pan; save second until needed.

In a medium saucepan, whisk together sugar, starch, and salt. Add the eggs, one at a time, whisking until smooth and no pockets of sugar-starch remain before adding the second. Whisk in vanilla bean paste, and then, very gradually, whisking the whole time, pour in milk, then cream. Bring mixture to a simmer over medium heat, whisking the whole time. As the custard begins to bubble, it will thicken. Remove from heat and stir in the butter until it is fully melted.

Immediately pour the warm custard into the baking pan over the first sheet of puff pastry and spread evenly. Place the second sheet of pastry on top, pressing gently to secure in place. Wrap the pan in plastic and refrigerate for at least 4 hours or overnight to allow the custard to fully set. Once chilled and set, use the foil to carefully lift the mixture from the tin. Dust with powdered sugar and then use a sharp, serrated knife to cut it into slices.