In the bowl of a stand mixer fitted with the dough hook, combine warm water and active dry yeast. Let sit for about 5 minutes to allow the yeast to become foamy.
Add salt, sugar, butter, and egg. Mix on low speed just to combine.
With the mixer on low speed, gradually add the flour to the bowl. Once the flour has been incorporated into the dough, allow the dough hook to knead the dough for about 3-5 minutes, until it's smooth and pulling away from the sides of the bowl.
Transfer dough to an oiled bowl and turn the dough to coat. Cover the bowl lightly with plastic wrap or a clean tea towel. Set in a warm place and let the dough rise until doubled in size, about 1 hour.
Punch down the dough and turn it out onto a floured surface. Using a floured rolling pin, roll the dough out into a large rectangle. The dough should be about 1/4-1/2" thick.
Prepare the dough for the filling by brushing with melted butter. In a small bowl, mix together sugar and ground cinnamon, then sprinkle it over the melted butter.
Starting at the long edge, tightly roll the dough away from you to create a "log" shape. Cut off the uneven edges of the log, then cut it into 12 pieces.
In a small mixing bowl, prepare the topping by stirring together the brown sugar, melted butter, warm water, and chopped pecans.
Spray a muffin pan with nonstick spray, then divide the pecan mixture among the 12 wells of the muffin pan. Place a round of cut dough over the top of the pecan mixture in each well.
Transfer to a warm place and let the rolls rise for about 30 minutes. Meanwhile, preheat the oven to 375F.
Once the rolls have completed their rise, transfer the pan to the preheated oven and bake for about 18-22 minutes, or until golden-brown.
Remove from oven and immediately invert onto a serving plate. If any of the pecan mixture remains in the pan, spoon it over the rolls while still warm. Enjoy warm or allow to cool completely.