Make the dough. Place flour in the bowl of a stand mixer. Add in sugar, yeast and salt in little piles in separate places over the flour in the bowl so that they are not touching.

Add in the egg, oil, milk and soft butter. Attach the dough hook and mix on medium-low for 10-15 minutes. Stop after a 2 minutes to scrape down the sides of the bowl and ensure all of the flour is incorporated and the dough is a uniform mixture.

Transfer the dough to a lightly floured work surface. Stretch and fold the dough to help develop the gluten structure.

Place the ball into a bowl and rub a little bit of oil lightly over the surface. Cover the bowl with plastic and then cover with a kitchen towel. Let it rise for 1-2 hours until nearly tripled in size.

While the dough is rising, prepare the pan and make the filling. Combine brown sugar, cinnamon and flour in a small bowl and mix well. Add melted butter and water and stir until it forms a smooth sludge.

Lightly flour a work surface. Invert the bowl and tip the dough out onto the surface. Gently pull on the dough and stretch it out into a rectangle shape, then roll it out to a 14x17 inch rectangle.

Gently apply the filling, spreading it out evenly right to the edges. Roll it up into a log and slice the log into 12 portions.

Place each roll spiral-side-up into the prepared pan. Cover the pan loosely with plastic and proof for 30 minutes to 1 hour.

Preheat the oven to 350°F.

Bake for 20-25 minutes until evenly golden and the center roll is cooked through. Let rolls cool for at least 20 minutes.

Make the icing. Combine cream cheese, soft butter, powdered sugar and vanilla in a medium bowl and mix until very smooth. Spread icing over each roll.