In a large bowl (or the bowl of the electric mixer) mix water, yeast, sugar, salt, eggs, oil, rum and vanilla. Add the rest of the ingredients and mix well (do not knead) using your hands, wooden spoon or electric mixer. The dough will be soft but will firm up after proving.
Cover with a tea towel and let rise for 2 hours in a warm place, away from drafts.
Divide the dough into 3 equal parts. Sprinkle with flour and shape each one into a ball, seam side down.
Dust the worksurface with flour and roll out each ball into an oval. Fold them over into thirds (watch reel). Transfer to a baking sheet lined with parchment paper, cover with plastic wrap or tea towel, and let them rise for 1 ½ hours.
Preheat oven at 180°C/350°F. Remove the plastic wrap and brush with a slightly beaten egg. Bake for 30-40 minutes or until golden brown. Let them cool completely and dust with powdered sugar.