Mix butter, sugar and salt in a large bowl until well combined. Add egg and mix until combined. Add in flour and Rapid Rise yeast, stir to combine. Add in milk and mix well and until soft smooth dough forms. Turn out on lightly floured surface. Knead a 10-12 times then place into a large bowl that has been well oiled. Cover and let dough rise in a draft free location for at least 30 minutes or until almost doubled in size.
Once risen, punch down dough and let rest for five minutes. Roll into a 14 x 8-inch rectangle (approximately) on a lightly floured surface. Brush with softened butter for filling. Combine cup sugar, brown sugar and cinnamon. Sprinkle over buttered dough. Roll up from long side. Cut into 12 cinnamon rolls.
Place cinnamon rolls in 13x9 inch pan that has been brushed with butter. At this point you can cover the rolls with plastic wrap or foil and place rolls in the fridge to bake the following morning. Or, preheat your oven to 350 degrees F and let the dough rise for 30 minutes, then bake.
If placing rolls in the fridge, remove from fridge 30-60 minutes prior to the time you will start baking them (60 minutes is best). Let them rest in a warm, draft free location. Preheat oven to 350 degrees. Once oven is heated, bake rolls for approximately 20 minutes (or until lightly browned). Remove from oven and frost immediately.