In a small bowl, stir together the yeast, warm water, and 1 tablespoon of the sugar. Let stand until foamy, about 10 minutes.

In the bowl of a stand mixer fitted with the dough hook, combine the flour, remaining sugar, egg, milk, and the yeast mixture. Mix on low speed until a shaggy dough forms. Add the butter and salt, and knead on medium speed until the dough is smooth and slightly sticky, about 10 minutes. Cover the bowl and let the dough rise in a warm place until doubled in size, about 1 hour, or refrigerate overnight.

To make the filling, in a medium bowl, combine the butter, cocoa powder, demerara sugar, and confectioners’ sugar. Mix with a spatula until mostly smooth. Add the chocolate spread and oil, and stir until fully combined and spreadable.

Once the dough has risen, divide it in half. Lightly flour a work surface and roll out one piece into a medium-thick rectangle, about 12 by 14 inches. Spread half of the cocoa filling over one half of the dough. Fold the dough in half lengthwise and press gently to seal. Lightly flour both sides and roll again into a large rectangle. Spread half of the remaining filling over one half and fold again. Roll once more into a thin rectangle, about 1/8-inch thick.

Using a pizza cutter or sharp knife, slice the dough into even strips, then cut each strip into triangles. Roll each triangle up from the wide end toward the tip, stretching gently as you roll. Repeat with the remaining dough and filling.

Arrange the rugelach seam-side down in a greased 9-inch/23 cm round or square cake pan, packing them tightly together. Cover and let rise for 30 to 45 minutes, until slightly puffed.

Heat the oven to 350°F (180°C). Brush the tops with beaten egg and bake until golden brown and crisp at the tips, 30 to 40 minutes.

While the rugelach bake, make the syrup. In a small saucepan, combine the sugar and water. Bring to a boil over medium heat, stirring until the sugar dissolves. Remove from heat.

As soon as the rugelach come out of the oven, brush them generously with the hot syrup. Let cool in the pan for at least 15 minutes before serving warm or at room temperature.