In a small bowl, gently whisk together the warm water, yeast, and 1 tablespoon of the sugar. Let stand for 5 minutes, or until a foams develops on the surface.
Meanwhile, generously flour a clean work surface. Gather two large glass mixing bowls (one for mixing and one for rising). Lightly grease one bowl.
Add the flour and salt to the un-greased mixing bowl. Whisk together and then create a well in the center and set aside.
In a small saucepan, melt 5 tablespoons of the butter. Remove from the heat and whisk in the milk, ¼ cup of the sugar, and the vanilla. The mixture should be warm but not hot. If it's hot, let it cool off before moving on to the next step.
Then, pour the mixture into the bowl with the flour. Add the yeast mixture and use a large wooden spoon to stir and mix until all of the flour has been incorporated.
Turn the dough out onto the floured surface. Knead for 8 to 10 minutes, or until the dough is smooth, springy, and elastic, adding more flour as needed. You'll know it's ready when it begins to hold its shape and springs back when pressed.
Shape the dough into a ball and place it in the greased bowl. Cover the bowl with a clean kitchen towel and let the dough rise in a warm place for 1 hour, or until doubled in size.
When the dough has just a few minutes left to rise, lightly grease a 9- by 13-inch casserole dish with oil. In a medium mixing bowl, whisk together the remaining ½ cup sugar and cinnamon. Melt the remaining 3 tablespoons butter in a pan or in the microwave. Set aside.
Turn the dough out onto a clean, generously floured work surface. Use a rolling pin to roll the dough into a rectangle that is approximately 12 x 24 inches in size.
Lightly brush the top of the dough with the melted butter and sprinkle with the sprinkles first, then the sugar-cinnamon mixture, leaving a ½-inch perimeter around the edge of the dough.
Starting at the front of the long edge of the rectangle, carefully roll the dough away from you until you have a tightly wound roll. Use your fingers to pinch the seam closed. Use a sharp serrated knife to slice the roll into 12 2-inch-thick rolls.
Gently transfer the rolls to the greased baking pan, swirled-side up, leaving ½ an inch of space between each. Loosely cover the pan with parchment paper and let the rolls rise in a warm place for 45 minutes, or until doubled in size.
Meanwhile, preheat the oven to 350F.
Bake for 22 to 26 minutes, or until the rolls are just barely turning golden and the tops feel firm to the touch.