In a large bowl, whisk together 1 cup of the flour, sugar, yeast, and salt. Add the warm milk, melted butter, and beaten egg. Mix until well combined.
Gradually add the remaining 1.5 cups of flour, mixing until a soft dough forms. Turn the dough out onto a lightly floured surface and knead for 6-8 minutes until smooth and elastic.
Place the dough in a lightly greased bowl, cover with plastic wrap, and let it rise in a warm place for about 1 hour, or until doubled in size.
While the dough is rising, prepare the filling. In a small bowl, mix together the softened butter, brown sugar, and cinnamon until well combined.
Once the dough has risen, punch it down and turn it out onto a lightly floured surface. Roll the dough into a large rectangle, approximately 12x18 inches.
Spread the cinnamon-sugar filling evenly over the dough, leaving a small border around the edges.
Roll up the dough tightly, starting from one of the longer sides. Cut the rolled dough into 8 equal slices.
To cook, you can wrap each roll in foil and cook over the campfire coals for about 10-15 minutes, turning occasionally, until golden brown and cooked through. Alternatively, bake in a preheated oven at 375°F (190°C) for 15-20 minutes.
While the rolls are cooking, prepare the glaze. Whisk together the powdered sugar, milk, and vanilla extract until smooth.
Once the cinnamon rolls are done, remove them from the heat and drizzle with the glaze.
Notes
These are best enjoyed warm! You can also wrap them in foil and place them directly in the embers of a campfire for a smoky flavor.