DOUGH: In a large bowl, whisk together 2 cups of the flour, sugar, yeast and salt.
Melt the butter in a small saucepan or medium bowl in the microwave. Remove from the heat and stir in the milk, water and vanilla. Pour the butter mixture over the flour mixture and mix with a spatula until combined.
Whisk the eggs in a small bowl, then add to the dough, mixing until the eggs are fully incorporated. Add the remaining ¾ cup, plus 1 tablespoon of flour and mix until combined.
Turn the dough out onto a floured work surface. Knead the dough for 10 minutes or until smooth and elastic. Shape it into a ball and place it in a lightly greased bowl. Cover the bowl with plastic wrap and let sit in a warm place until the dough has doubled in size, about 1 hour.
FILLING: Combine the brown sugar, allspice, and cinnamon in a small bowl.
FROSTING: Combine the cream cheese and butter; beat on medium-high speed until well blended and there are no visible lumps of cream cheese. Reduce the speed to medium and gradually add the icing sugar, then beat on high speed until completely smooth. Use milk to create a smooth and pourable consistency.
Grease a 9×5-inch loaf pan.
Punch down the dough and turn it out onto a floured work surface. Knead the dough for a couple of minutes, adding a touch of flour if it is sticky. Pat it into a rectangle approximately 12×20 inches. Spread a generous amount of the soft butter all over the dough. Sprinkle the cinnamon sugar filling evenly over the entire buttered surface. Use a pizza cutter or sharp knife to cleanly cut the dough into six strips, 2-inches wide and 20-inches long. Gently stack the strips on top of each other. Cut across the pile to create six equal stacks.
With the cinnamon side facing inward, stand two rectangles upright in the pan, touching one side of the pan. (The dough rectangles will not fill the width of the pan.) Place another two rectangles so they touch the other side of the pan. Continue to alternate the rectangles, making sure the cinnamon sides face the same direction, except for the last rectangle, which should face inward. Cover with a tea towel and let sit in a warm place to rise until doubled, about 45 minutes.
Preheat the oven to 350 F. Bake for 30 minutes, or until the top of the bread is dark golden brown. For even baking, rotate the pan front to back halfway through.
Remove from oven and allow the bread to cool slightly in the pan.
Spoon the cream cheese glaze over the top of the warm loaf. The loaf can be covered and stored in the fridge for up to three days.