Combine 2 cups of water, yeast, sugar and salt in a large mixing bowl or in the bowl of the stand mixer. Whisk well.
In a small saucepan, heat butter and milk; cook till the butter is melted. Turn off the heat and let cool for a couple of minutes. Add water and vanilla extract. Mix well.
Add the egg replacer mixture (or whisked eggs) and the melted butter to the dry ingredients in the bowl. Mix and knead to form a sticky dough. Add ½ cup of wholewheat flour and knead to form a soft, pliable dough. If the dough seems sticky, then add in the remaining ½cup of all purpose flour 1tbsp at a time. Knead for 5~7 minutes.
Transfer the dough into a lightly greased bowl, cover and set aside to rise until doubled in volume, about 1 hour.
In the mean time, combine sugar, ground cinnamon and ground nutmeg for the filling. Melt the butter and keep ready.
Gently deflate the dough and roll it out into a 12"x20" rectangle. Brush the butter liberally over the dough and sprinkle the cinnamon sugar evenly all over.
Cut the dough into 6 equal pieces -- stack the pieces one on top of the other. Then cut the stack into 6 equal pieces. Place the pieces in a greased 9"x5" loaf pan. Cover with a plastic wrap and kitchen towel for 30~45 minutes.
Preheat the oven to 350°F. Bake for 30~35 minutes until the top is golden brown and the bread is baked through. Remove from the oven and let cool for 20 minutes. Run a knife around the edges of the bread and turn over onto a plate to cool slightly. Enjoy warm, for the best taste. Leftovers can be stored in an airtight container for up to 2 days.