Special equipment: One 9-inch square baking pan, preferably non-stick, buttered on sides only; one sheet pan, lined with aluminum foil
Place the yeast and warm water in a small bowl and stir with a fork to dissolve the yeast. Allow it to stand for about 3 minutes.
Mix the flour and salt together in a large bowl. Add the warm water and the yeast mixture and stir with your fingers to moisten the flour, scraping the sides of the bowl and folding the dough over itself until it gathers into a shaggy mass.
Move the dough to a lightly floured surface and knead it by hand for 5 minutes. This is a soft, moist dough. If the dough seems too stiff and hard to knead, add extra warm water 1 tablespoon at a time until you get a nice malleable dough. Gently shape the dough into a loose ball, cover it with plastic, and let it rest on the table for 20 minutes. (This rest period is the autolyse.)
Gently knead the dough on the lightly floured surface for 1 to 2 more minutes, or until it becomes smooth, supple, and elastic but not too firm. The texture of the dough should be soft but springy. Shape the dough into a loose ball, place it in a lightly oiled bowl, and turn to coat the top with oil. Cover it tightly with plastic wrap and let it rise at room temperature (75 to 77 degrees F) until it has doubled in volume, about 1 1/2 to 2 hours.
While the dough is rising; in a small saucepan, heat the 9 tablespoons butter and the dark brown sugar over low heat, stirring occasionally, until the butter has melted and the sugar is completely moistened (it won't be dissolved), then whisk until the mixture looks silky and a little lighter in color. Use 1 tablespoon softened butter to grease the sides of a 9-inch square pan, then pour in the caramel, tilting the pan slightly so the mixture spreads evenly over the bottom of the pan. Sprinkle the toasted pecans over the warm caramel and press them down slightly. Put the pan in the refrigerator to cool the caramel; be the pan's on a level surface. Put the granulated sugar and cinnamon in a small bowl and stir until evenly mixed. Set aside.
When the dough has doubled, gently pour it out of the bowl onto the floured work surface. Flatten the dough and stretch it with your fingers to form a 13 by 10-inch rectangle, with a longside facing you. Work gently so you don't tear the dough surface. The dough should stretch easily at this point, but if it resists, let it rest for 5 minutes and resume stretching. Check to be sure the dough isn't sticking to the work surface; flour the table again, if necessary.
Spread 3 tablespoons of the softened butter evenly over the dough, leaving a 1/2-inch strip unbuttered along the top edge. Sprinkle the cinnamon/sugar mixture generously and evenly over the butter, again leaving the top 1/2-inch of the rectangle bare. Starting with the bottom edge, roll up the dough jelly-roll fashion into a long log. If the dough sticks to the table as you're rolling, use a dough scraper to loosen it gently. Pinch gently but firmly along the seam to seal it. If necessary, gently shape the roll so it is a nice uniform log.
Take the caramel-lined pan out of the refrigerator. Cut the log of dough into 9 equal pieces. (It's easiest to mark the roll first to show where you're going to make the cuts--a slight indentation with the knife edge will do--then use a sharp serrated knife to cut completely through the dough.) Lay the pieces cut side down on top of the caramel. Don't worry if it's a tight fit. Let rise, uncovered, at room temperature until the dough has almost doubled, about 1 to 1 1/4 hours. The rolls should fill the pan and extend 1/2 to 3/4-inch above it. In the meantime, position a rack in the center of the oven and preheat the oven to 375 degrees F. Put the pan of sticky buns on a foil-lined baking sheet and place it in the oven. Bake for 10 minutes, then reduce the oven temperature to 350 degrees F and bake for 30 to 40 minutes longer, until the tops of the buns are golden brown and crusty. It's important to bake the buns long enough so the dough is cooked all the way through and the caramel topping develops properly. Set the pan of buns on a rack to cool for 5 minutes. Then quickly but carefully turn the pan upside-down and release the sticky buns onto a large flat heatproof plate. Immediately scrape out any hot caramel remaining in the bottom of the pan and spread it on the tops of the buns, filling in any bare spots. Let them cool until just warm before serving. (Clean the pan by soaking it in very hot water to dissolve the caramel.) Store any leftovers covered in plastic wrap at room temperature.