1 large sweet potato (about 12 oz.), peeled and cut into 1/2-inch pieces (about 2 1/2 cups)
2/3 cup whole milk
1/4 cup warm water (100°F to 110°F)
1 (1/4-oz.) package active dry yeast
3 tablespoons + 1 teaspoon granulated sugar, divided
2 large eggs
6 tablespoons butter, melted, divided
4 1/2 cups bread flour, plus more for kneading
1 1/2 tablespoons kosher salt
2 tablespoons cane syrup
3/4 teaspoon flaky sea salt
Bring sweet potato and milk to a boil in a small saucepan over medium-high. Reduce heat to medium-low. Cook, covered, stirring occasionally, until potatoes are very soft, about 20 minutes. Remove from heat. Using a potato masher or fork, mash potatoes with milk until very smooth. Transfer to a medium bowl to cool completely, about 30 minutes.
Stir together warm water, yeast, and 1 teaspoon of the sugar in a small bowl. Let stand until foamy, about 5 minutes.
Beat together sweet potato mixture, yeast mixture, eggs, 4 tablespoons of the melted butter, and remaining 3 tablespoons sugar in the bowl of a stand mixer fitted with a dough hook on low to combine. With mixer running, gradually add bread flour and kosher salt, beating on low until dough is soft and smooth, about 4 minutes. Transfer dough to a lightly floured surface. Knead until smooth and elastic, about 5 minutes, adding up to 1/3 cup flour, as needed, if dough is very sticky. Transfer dough to a lightly greased large bowl, and cover with plastic wrap. Let stand at room temperature until doubled in size, 1 to 1 1/2 hours.
Preheat oven to 375°F. Turn dough out onto a lightly floured surface, and divide into 15 balls. Place balls in a lightly greased 13- x 9-inch baking pan. Cover with plastic wrap, and let stand at room temperature until almost doubled in size, 45 minutes to 1 hour. Meanwhile, stir together cane syrup and remaining 2 tablespoons melted butter; set aside.
Uncover rolls, and bake in preheated oven until light golden brown, 18 to 22 minutes. Brush hot rolls with cane syrup butter; sprinkle with flaky sea salt. Serve immediately, or transfer rolls to a wire rack to cool completely, about 30 minutes.