Whisk one-third of the warm oat milk with the egg yolks, sugar, vanilla, and cornstarch in a mixing bowl until smooth.

Whisk the mixture into the remaining warm oat milk, then cook over low to medium heat, whisking constantly, until the pastry cream thickens.

Remove from the heat and add the cold cubes of vegan butter. Divide the pastry cream in two: one half for the chestnut pastry cream and the other for the chocolate pastry cream.

Whisk half of the hot pastry cream with the chocolate chips until the chocolate melts and the mixture is smooth. Blend with an immersion blender for an extra-silky chocolate pastry cream.

If the pastry cream is not hot enough, melt the chocolate first, then stir it into the pastry cream until smooth.

Cover with plastic wrap and refrigerate for at least 3 hours.

Blend the chestnut purée with the remaining pastry cream using an immersion blender until completely smooth. You can also use a food processor.

Shape the chestnut cream into a log by wrapping it in plastic wrap and forming it into a cylinder 23 cm long and 2.5 cm in diameter. If you like, add chopped toasted nuts for crunch.

Freeze until firm enough to assemble the yule log. Cover the remaining chestnut cream with plastic wrap and refrigerate for at least 3 hours.

Preheat the oven to 170°C.

Sift all the dry ingredients into a mixing bowl and whisk to combine.

Whip the egg whites with the sugar to make a meringue, then set aside.

Add the oat milk to the dry ingredients and whisk by hand or with an electric mixer until smooth. Fold in the meringue in 3 additions.

Spread the batter in a layer about 1/2 cm thick on a baking sheet lined with parchment paper, then bake for 12-15 minutes.

Let the sponge cool completely. Trim away the dry edges before using.

Melt the dark chocolate and spread it in a thin layer over cake acetate strips or strips of parchment paper, each 2.5 cm wide and 30 cm long.

Place the strips on a slightly curved or flat surface, then let the chocolate set in the refrigerator or at cool room temperature.

Trim the dry edges from the sponge. The sponge should measure 28 cm wide and 38 cm long. Place it on parchment paper, then pipe alternating lines of chestnut and chocolate pastry cream over the surface, leaving a 1 cm border around the edges.

Place the frozen chestnut log along the edge where you will start rolling.

Start rolling, keeping gentle tension on the paper to support the roll all the way along, and use your fingers at the ends to make the first fold. Lift the parchment paper up and forward to roll the sponge, using the paper to press gently and keep the roll tight. Keep the seam underneath.

Refrigerate the rolled yule log, still wrapped in the parchment paper, for 30 minutes.

Trim both ends of the yule log to reveal an even filling. Transfer to a cake board or serving plate. Pipe alternating lines of chestnut and chocolate pastry cream over the entire surface.

Arrange the chocolate bark strips over the pastry cream lines to completely cover the yule log. Dust lightly with icing sugar just before serving or slicing.