Dissolve yeast in warm water in a large bowl. Add oil and sugar and let stand 5 minutes.
Add egg and salt to yeast mixture and stir.
Gradually stir in flour, making a soft dough.
Turn out onto lightly floured surface and knead until elastic and smooth. (Approximately 4-5 minutes)
Place in a lightly oiled bowl. Cover and let rise in a warm place for 30 minutes.
Turn out on a lightly floured surface and roll into a 12x15-inch rectangle.
Spread dough with 1½ tablespoons softened butter.
Fold in half 3 times.
Roll into a 12x15-inch rectangle again.
Spread additional 1½ tablespoons softened butter evenly over all the dough.
Top with brown sugar and cinnamon.
Starting on the long side, roll dough into a long tube.
Slice tube into approximately 12 rolls. Place on a baking sheet lined with parchment paper, leaving space between rolls to allow for rising.
Top cinnamon rolls with pecans. Sprinkle lightly with cinnamon and sugar.
Preheat oven to 425ºF. Let rolls rise for 15 minutes.
Bake rolls 12-15 minutes or until golden.
While rolls are baking, follow directions to make the icing.
Remove rolls from oven and cool for 10 minutes before topping with the icing.