In a small bowl, combine the yeast, sugar, and warm plant-based milk. Stir and let stand for 10 minutes, until foamy and activated.
Transfer the mixture to the bowl of a stand mixer fitted with the dough hook. Add the remaining dough ingredients except the butter. Mix on low speed until a dough begins to form, then increase to medium speed. Add the butter gradually, one cube at a time, mixing until fully incorporated. Continue kneading for 10 to 12 minutes, until the dough is smooth, elastic, and supple.
Lightly oil a large bowl and place the dough inside. Grease the surface of the dough, cover with plastic wrap, and let rise for 1 to 1½ hours, or until doubled in size.
Meanwhile, prepare the filling by stirring together the soft butter, cocoa powder, and powdered sugar in a medium bowl until smooth and creamy.
Preheat the oven to 340°F (170°C). Grease two 9-inch/22 cm cake rings and place them on a parchment-lined baking sheet.
Lightly flour a work surface and turn out the risen dough. Divide in half. Roll each piece into a large rectangle.
Spread half of the cocoa filling over half the surface of one rectangle. Fold it over like a book to enclose the filling. Gently roll again to form a thinner rectangle. Spread a layer of chocolate spread over the full surface. Fold in half once more, press to seal, and roll out to a thin rectangle again. Trim the edges and cut into long triangles using a pizza cutter. Roll each triangle into a rugelach shape.
Place the rolled rugelach into the prepared rings. Cover with a damp towel and let rise for 30 minutes.
To make the sugar syrup, combine the sugar and water in a small saucepan. Bring to a boil, then simmer for 2 minutes. Remove from the heat and cool completely.
Bake the cakes for 25 to 35 minutes, until deeply golden. Remove from the oven and brush immediately with the cooled sugar syrup. Serve warm or at room temperature.