Spray a 9×13-inch baking pan with cooking spray.
For the caramel-pecan glaze: In the bowl of a stand mixer fitted with a paddle attachment, or using a hand mixer, mix together the butter, granulated sugar, brown sugar and salt on medium speed for 2-3 minutes, until light and fluffy.
Add the corn syrup and vanilla, and continue to mix for 5 minutes, until light and fluffy.
Spread the glaze into an even layer in the prepared pan. Sprinkle with the chopped pecans.
For the sticky bun dough: In the bowl of a stand mixer fitted with the paddle attachment, add the gluten-free bread flour, sugar, instant yeast, salt and baking powder. Mix to combine.
With the mixer running on low, slowly add the water, milk, eggs and melted butter. Increase the speed to medium and mix for 3 minutes. The dough will resemble thick cookie dough, this is normal.
Using an oiled rubber spatula, scrape down the bottom and sides of the bowl. Cover the bowl tightly with plastic wrap and refrigerate for 20 minutes. (Refrigerating the dough makes it easier to roll out.)
Turn out the dough onto a lightly floured surface and shape into a ball. Sprinkle with a little gluten-free flour, then roll the dough out into a 15×15-inch square.
For the filling: In a small bowl, mix together the sugar and cinnamon. Sprinkle the cinnamon-sugar filling all over the dough.
Using a pizza cutter, cut the square into twelve 1¼-inch-wide strips.
Roll each dough strip up into a spiral. Place in the prepared baking pan on top of the caramel-pecan glaze.
Cover the pan with oiled plastic wrap and place in a warm place. Allow the rolls to rise for 45-60 minutes.
Preheat the oven to 350°F. Remove the plastic wrap. Bake for 30-35 minutes, until the rolls are slightly golden brown.
Remove from the oven and cool in the baking pan for 15 minutes before turning them out onto another pan or serving platter. Spoon any run-off glaze back over the buns. Cool for another 20 minutes before serving.