Into a stand mixer, mix together the milk, instant dry yeast, brown sugar, eggs, butter and salt. Switch to the dough hook, add flour and mix until a dough forms. Cover the bowl with a towel and rest for 1 hour.
Spray a 9×13 baking dish with nonstick cooking spray. Set aside.
In a saucepan, combine the brown sugar and butter. Bring to a boil over medium heat and simmer for 4 minutes. Remove from heat, stir in rum. Pour mixture into the baking dish and top with the chopped pecans. Set aside.
In a bowl, mix together brown sugar and cinnamon until all is combined. Set aside.
Lightly sprinkle your work surface with flour. Transfer the dough onto your work surface and roll into a rectangle with the long. Brush melted butter over the dough. Sprinkle the cinnamon brown sugar mixture evenly over the melted butter. Roll the dough into an 18-inch long log. Using a sharp knife, cut into 12 rolls. Transfer the rolls on top of the rum toffee pecan topping in the baking dish. Cover the rolls with a towel and let them rise for 30 minutes.
Preheat the oven to 375 degrees F. Bake the rolls for 25-30 minutes or until golden brown on top. At the 12 minute mark, cover the top of the rolls with aluminum foil to avoid them browning too much. Remove from oven and let them cool for 5 minutes.
After 5 minutes, carefully invert the rolls onto a large serving dish. Serve warm. Enjoy!
To make these sticky buns overnight: Once you transfer the buns to the baking dish on top of the rum toffee pecan topping, brush the tops of the sticky buns with melted butter then cover the dish in plastic wrap. The butter will help the plastic wrap come off easily the next day. Place the dish in the fridge overnight for 8-12 hours. Once you're ready to bake, bring the sticky buns to room temperature, about 30 minutes or so, before baking.