Combine 1/4 cup warmed apple cider with yeast. Set aside until foamy.
In a large bowl (I use my stand mixer) combine remaining ingredients, except remaining apple cider.
Add in apple cider and yeast mixture and 1/2 cups apple cider. Mix together, adding in remaining apple cider if needed.
Knead mixture for 7-10 minutes. Shape into a ball, place back into bowl, and let rise for an hour, until doubled.
While the dough is rising add diced apples, brown sugar, cinnamon and apple cider in a skillet. Cook over medium low heat until apples are tender. Add in more water or apple cider if needed to cook apples down. However, you do not want too much remaining liquid.
After the dough has doubled, place onto counter and roll into a rectangle approximately 20 x 15 inches.
Spread the apple butter on the dough and top with cooked apples.
Roll dough into a log shape, and cut into 12 rolls approximately 1.5 inches wide.
Place on a baking sheet and allow to rise for another hour.
Bake at 350 for 25-30 minutes.
While the rolls bake make the frosting. In a small saucepan over medium heat melt the butter. Let it simmer until it is foamy, stir and let simmer until you can start to see brown specks. This will take about 5-10 minutes.
In a large bowl combine cream cheese, powdered sugar and browned butter. Whisk until combined adding in apple cider to get a smooth pourable consistency.
Remove rolls from the oven, pour frosting over the top and enjoy!