Make the dough Preheat the oven to 425°. Pierce the sweet potatoes all over with a fork, and wrap each potato tightly in aluminum foil. Place on a baking sheet and bake until tender, about 1 hour. Let cool slightly, and discard the foil. Halve the potatoes lengthwise. Spoon the flesh into a medium bowl and mash with a fork. Discard the skins.
In a small saucepan, warm the milk over moderate heat until bubbles appear around the edge; remove from the heat. In a small bowl, whisk the yeast into the warm water, and let stand until bubbly, about 10 minutes.In a large bowl, combine the warm milk with the yeast mixture, 2 cups of the flour, 1 tablespoon of the sugar, and the salt. Let stand in a warm place until bubbly, about 15 minutes.
In a stand mixer fitted with the paddle attachment, beat the shortening with the remaining 3/4 cup of sugar at medium speed until light and fluffy, about 4 minutes. Beat in the eggs, one at a time. Beat in 3/4 cup of the mashed sweet potato and the orange zest; reserve the remaining potato for the filling. Beat in the bubbly milk mixture and the remaining 3 cups of flour at medium-low speed until a smooth, sticky dough forms, about 4 minutes. Scrape the dough into a large bowl. Cover with plastic wrap, and let stand in a warm place until the dough has doubled in size, about 1 hour and 30 minutes.
Make the filling Preheat the oven to 425°. Spread the pecans on a small rimmed baking sheet, and bake until browned, about 6 minutes, stirring halfway through. Transfer the pecans to a food processor, let cool, then pulse until finely chopped. Add 1/2 cup of the reserved mashed sweet potato, the stick of butter, sugar, maple syrup, and salt, and pulse until smooth. Scrape the filling into a small bowl.
Make the salted pecans In a medium skillet, melt the butter. Add the pecans, and cook over moderate heat, stirring, until golden, about 4 minutes. Scrape onto a plate, and season with the salt.
Make the buns Turn the dough out onto a generously floured work surface, and cut the dough in half. Working with 1 piece at a time, roll out the dough to a 9-by-7-inch rectangle, about 1/4 inch thick. Spread half of the filling over the dough, leaving a 1-inch border. Sprinkle one-fourth of the salted pecans evenly over the filling. Brush one long side with water. Starting from the opposite long side, roll up the dough into a tight log, and pinch the ends to seal. Transfer to a baking sheet and refrigerate until chilled, about 20 minutes. Repeat with the remaining dough, filling, and one-fourth of the salted pecans.
Generously brush two 9-inch square metal cake pans with butter. Transfer the logs to a work surface, and cut each crosswise into 6 equal slices, about 1 1/2 inches thick. Arrange the buns, cut side up, in the prepared cake pans. Cover the pans with plastic wrap, and let the buns rise in a warm place until almost doubled in size, about 40 minutes.
Meanwhile, make the caramel In a small saucepan, combine the sugar with 1/2 cup of water. Bring to a boil, and cook over moderately high heat, swirling the pan occasionally, until deep amber, 6 to 8 minutes. Remove the pan from the heat, and carefully whisk in the butter. Gradually whisk in the milk and salt. Return the pan to moderately high heat, and simmer until the caramel has thickened slightly, about 1 minute. Keep warm.
Make the cinnamon butter In a small saucepan, melt the butter. Remove the pan from the heat, and stir in the cinnamon. Keep warm.
Preheat the oven to 375°. Remove the plastic wrap from the cake pans, and bake the buns until golden and risen, about 25 minutes. Immediately brush the buns with the warm cinnamon butter, and drizzle with the warm caramel. Sprinkle the buns with the remaining salted pecans. Let cool slightly, and serve warm.
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