In a small bowl, dissolve the yeast in ¼ cup (60ml) lukewarm water. Let it sit for 10 minutes. The mixture should become foamy, which means the yeast is active.
In a separate bowl, whisk together brown sugar, cinnamon and nutmeg for filling. Set aside.
In a large mixing bowl with paddle attachment, whisk together 4 cups of flour, sugar and salt. (If you’re not using a stand mixer, simply use a whisk.) Add yeast mixture, butter, milk and egg and mix until the soft dough forms. Put on a lightly floured surface and knead for at least 8-10 minutes until smooth. Place the dough in a lightly oiled bowl, cover with damp towel and place in warm place to rise for 1 hour, or until doubled in size. (I usually put the bowl in a microwave with a glass of hot water.)
Once the dough is doubled in size, put on a floured surface and punch it down. Roll the dough out into a rough rectangle. Place 1 ½ cups of shredded apple in the middle and fold the dough over. Sprinkle ¼ cup of flour over the dough and knead until the apple is evenly distributed. (This step is messy. Add a little more flour, if needed.)
Roll the dough out into a 15×19 rectangle. Spread the melted butter all over the rolled dough, and sprinkle sugar mixture from step 2. Roll up the dough into a log, and cut into 12 equal rolls. Put the rolls in greased 9x13in (23x33cm) baking pan. Cover it with a kitchen towel and let it rise for 30-60minutes, or until doubled in size.
Preheat oven to 350°F (177°C). Bake the rolls for 25-30 minutes, or until golden brown.
While the rolls are baking, make the apple caramel sauce. In a medium saucepan, melt the butter and add the remaining ½ cup of shredded apple and brown sugar. Once the sugar is melted, pour in heavy cream and cook for about 5-7 minutes, whisking frequently. Add vanilla extract and salt. Taste and make sure you’re happy with the flavor. Add more vanilla extract or salt, if needed. Cool slightly.
Pour half of the caramel sauce over the rolls 5 minutes before the rolls are done. Continue to bake for 5 minutes. Cool on wire rack. Serve with remaining caramel on the side.