In a large bowl, dissolve the yeast and sugar in warm milk. Let stand for 5 minutes, or until foamy.

Add melted butter, egg, and salt to the yeast mixture. Stir to combine.

Gradually add flour to the mixture, stirring until a dough forms.

Turn the dough out onto a floured surface and knead for 5-7 minutes, or until smooth and elastic.

Place the dough in a lightly greased bowl, cover with a clean kitchen towel, and let rise in a warm place for 1 hour, or until doubled in size.

While the dough is rising, prepare the filling. In a bowl, combine softened butter, brown sugar, and cinnamon.

Preheat the oven to 375°F (190°C). Grease a 9x13 inch baking pan.

Punch down the dough and roll it out on a floured surface into a 12x18 inch rectangle.

Spread the filling evenly over the dough, leaving a 1/2 inch border around the edges.

Sprinkle the apples and walnuts over the filling.

Starting from the long side, roll up the dough tightly.

Cut the roll into 12 even slices and place them in the prepared baking pan.

Cover the pan with a clean kitchen towel and let the rolls rise in a warm place for 30 minutes.

Bake for 25-30 minutes, or until golden brown.

While the rolls are baking, make the caramel glaze.

In a small saucepan, melt butter over medium heat. Add brown sugar and heavy cream. Bring to a simmer, stirring constantly.

Remove from heat and stir in vanilla extract.

Drizzle the caramel glaze over the warm rolls and serve immediately.