In a saucepan over medium heat, begin by heating the milk, water, sugar, and 1/4 cup butter. Stir until warm (about 120 degrees F) and the butter is almost melted. (Do not boil. If the liquid is too hot it will kill the yeast.)
Transfer this mixture to a large bowl and stir in the yeast. Let sit for about 10 minutes to activate, then whisk in the egg and vanilla.
Next, add in about 4 1/2 cups of flour and 1/2 teaspoon of salt. Mix until a dough forms. Then, knead the dough for about 8 minutes or until smooth and elastic. If the dough feels too sticky, add more flour as needed.
Transfer to an oiled extra-large bowl. Cover loosely with a kitchen towel or plastic wrap and let rise in a warm place until doubled in size. (About 1 to 1.5 hours.)
In the meantime, spray two 9-inch round cake pans with baking spray and set them aside.
To create the topping, add the brown sugar and butter to a small saucepan. Cook and stir over medium heat until the sugar dissolves. (This will take about 5 minutes. Do not boil.) Stir in the heavy cream and 1/2 teaspoon salt and remove from the heat.
Divide the sauce equally between the two prepared cake pans. Sprinkle evenly with the chopped pecans.
Once the dough has risen, divide it in half. Roll out each half into a 6 x 14-inch rectangle. For the filling, in a small bowl, mix together the brown sugar and cinnamon. Brush the 1/4 cup melted butter evenly over the dough, then sprinkle evenly with the brown sugar and cinnamon mixture.
Starting with a long side, roll each rectangle into a log.
Cut each log into 9 rolls. Arrange the rolls evenly in the pans prepared with the caramel and pecans. Each pan should have 9 rolls. Cover loosely and let the rolls rise in a warm area for about 30 minutes.
Preheat the oven to 375 degrees F. Place foil or baking sheet pans on the lower shelf of your oven as the caramel sauce will likely bubble over. Bake for 25 to 30 minutes or until browned and cooked through.
Immediately and carefully invert each pan onto a plate. Serve warm.