- Prepare the brioche dough: In a stand mixer bowl fitted with a dough hook, blend together flour, sugar, salt, and yeast on low until combined. Pour in the eggs and warm milk, mixing until dough comes together. Raise speed to medium-high and knead for about 5 minutes, until dough just starts separating from the bowl's sidesit will still be rather sticky.
- Lower the mixer speed and begin adding butter a chunk at a time, only adding more when the previous piece is combined, about 4-5 minutes total. Once all butter is incorporated, turn mixer back up to medium-high and knead until the dough is smooth, glossy, and slightly sticky, about 5 more minutes.
- Lightly oil a large bowl, transfer the dough, and turn it to coat in oil. Cover and let rise until it doubles, about 1 1/2 hours.
- While dough is rising, make the pastry cream: In a small saucepan, heat milk and sugar. Use a paring knife to split and scrape seeds from half a vanilla bean into the saucepan and add the pod as well. Warm over low heat until it starts to simmer and sugar dissolves, stirring gently. In a separate bowl, whisk egg yolks, cornstarch, and a pinch of salt. Gradually whisk in the hot milk, slowly, to avoid curdling the yolks. Once combined, return everything to the pan and cook on low, whisking constantly, until cream thickens, 2-3 minutes.
- Take off heat and strain through a fine-mesh sieve set over a medium bowl to remove the vanilla pod and any egg fragments. Place this bowl in a larger bowl with ice to chill the custard, stirring occasionally until cooled. Cover with plastic and refrigerate until ready to use.
- Gently deflate the risen dough and lay it onto a floured sheet of parchment that's roughly double the size of a standard baking trayabout 18 by 26 inches is ideal. Since the dough is sticky, parchment makes it easier to handle. Dust the dough with flour, place a second same-sized parchment on top, and roll out to an 8 by 24-inch rectangle, flouring as needed so it doesn't stick.
- Remove the upper parchment layer and rotate so the long side of the rectangle is closest to you. Spread the cooled pastry cream evenly over the lower half and scatter the chocolate chips on top. Dust this layer very lightly with extra flour. Using the parchment, fold the top half of dough over the pastry cream and pinch edges to seal.
- Line two baking sheets with parchment. Use a flour-dusted pizza cutter to slice the filled dough rectangle crosswise into 12 shorter rectangles. Lift these to the baking sheets. Flour your hands and pat the sides of each rectangle to shape and help seal, pinching gently so cream doesn't leak while baking. Loosely cover with plastic wrap and allow to rise until just slightly puffed, roughly 30 minutes.
- Meanwhile, arrange oven racks in the top and bottom thirds and preheat to 400F.
- For the egg wash: Beat together the egg, splash of milk, and a touch of salt. After the 30-minute rise, brush the wash over the tops and sides of the pastries. Bake for 20-22 minutes, swapping the trays between racks about halfway to ensure even browning, until golden and risen.
- As the pain suisse bake, create the syrup: In a small saucepan, combine the sugar and water. Split and scrape the vanilla bean seeds into it, adding the pod as well. Heat on medium until sugar has completely dissolved, then set aside.
- Once baked, brush the hot pastries generously with the vanilla syrup. Transfer to racks to cool. Pain suisse are wonderful served warm or at room temperaturetreat yourself and watch them disappear!
Note: When measuring flour, spoon into the measuring cup and level off the top instead of scooping directly from the bag to prevent overpacking and dry results. Generous flour use while shaping and assembling helps manage the sticky dough and keeps pastry cream from escaping in the oven.
