Preheat oven to 375 degrees F. Grease a 13x9 inch baking pan.
Put 2 cups of flour, sugar, yeast, and salt in a large mixing bowl. Then slowly stir in the warm water.
Add only two tablespoons of the softened butter and the egg, beating them until very smooth.
Then add the remainder of the flour slowly and stir until a soft dough forms.
Put plastic wrap over the top of the bowl and let the dough rise until doubled, about 30 minutes.
Flour a smooth surface, such as the table or countertop, and roll dough into a rectangle.
Spread the rest of the butter, which should be four tablespoons, on the dough.
In another bowl, mix cinnamon and brown sugar together and then sprinkle the mixture over the dough.
Roll the dough up into a tight roll, starting on the long side. Then cut into about 12 slices.
Put each cinnamon roll slice onto the baking dish. Cover and let rise until doubled, about 30 minutes.
Remove cover and bake for about 25 minutes at 375 degrees F. Remove from oven and put on serving dish.