For the dough, heat the milk, vegetable oil, and sugar in a medium saucepan over medium heat to just below a boil. Set aside and cool to warm. Sprinkle the yeast on top and let it sit on the milk for 1 minute.
Add 4 cups of the flour. Stir until just combined, then cover with a clean kitchen towel, and set aside in a relatively warm place for 1 hour. After 1 hour, remove the towel and add the baking powder, baking soda, salt, and the remaining 1 cup flour. Stir thoroughly to combine. Use the dough right away, or place in a mixing bowl and refrigerate for up to 3 days, punching down the dough if it rises to the top of the bowl. (Note: dough is easier to work with if it’s been chilled for at least an hour or so beforehand.)
Preheat the oven to 375°F.
To assemble the rolls, remove half the dough from the pan/bowl. (Optional: make dinner rolls with half the dough. Just be sure to adjust filling proportions if you do.) On a floured baking surface, roll the dough into a large rectangle. The dough should be rolled very thin.
To make the filling, spread the softened butter over the surface of the dough. Use your fingers to spread the butter evenly. Generously sprinkle the cinnamon, sugar, and chopped pecans over the butter. Gooey is the goal.
Now, beginning at the end farthest from you, roll the rectangle tightly towards you. Use both hands and work slowly, being careful to keep the roll tight. When you reach the end, pinch the seam together and flip the roll so that the seam is face down. When you’re finished, you’ll wind up with one long buttery, cinnamony, sugary, gooey log.
With a sharp knife, make 1/2-inch slices. Pour a couple of teaspoons of melted butter into disposable foil cake pans and swirl to coat. Place the sliced rolls in the pans, being careful not to overcrowd. (Each pan will hold 7 to 9 rolls.
Cover all the pans with a kitchen towel and set aside to rise on the countertop for at least 20 minutes before baking. Remove the towel and bake for 15 to 18 minutes, until golden brown. Don’t allow the rolls to become overly brown.
While the rolls are baking, make the icing: In a large bowl, whisk together the powdered sugar, milk, butter, coffee, and salt. Splash in the vanilla extract. Whisk until very smooth. Taste and add in more vanilla, sugar, butter, or other ingredients as needed until the icing reaches the desired consistency. The icing should be somewhat thick but still very pourable.
Remove pans from the oven. Immediately drizzle icing over the top. Be sure to get it all around the edges and over the top. As they sit, the rolls will absorb some of the icing’s moisture and flavor.