In a small saucepan over medium-high heat, combine the sweet potato pieces and milk. Bring to a boil, then reduce heat to medium-low. Cover and cook for 10-15 minutes, stirring occasionally, until the potatoes are very soft.
Remove from heat and mash the sweet potato with the milk until smooth. Transfer to a medium bowl and let cool for about 30 minutes.
In a small bowl, combine the warm water, yeast, and 1 teaspoon sugar. Let stand for about 5 minutes until foamy.
In the bowl of a stand mixer fitted with the dough hook, add the cooled mashed sweet potato, yeast mixture, eggs, melted butter, and remaining 3 tablespoons sugar. Mix on low until combined.
With the mixer on low, gradually add the salt and 4 cups of bread flour. Beat for about 4 minutes until the dough is smooth.
Turn the dough out onto a lightly floured surface. Knead by hand for about 5 minutes, adding the remaining ½ cup flour (or up to 1 cup total extra) a little at a time if the dough is too sticky.
Lightly spray a large bowl with nonstick spray. Place the dough in the bowl, cover with plastic wrap, and let rise in a warm, draft-free spot until doubled, about 1 to 1 ½ hours.
Spray a 9×13-inch baking dish with nonstick spray.
Punch down the dough, turn it onto a floured surface, and divide into 15 equal pieces.
Shape each piece into a smooth ball by cupping your hand over the dough and rolling it in a circular motion on the counter until the surface is taut and smooth.
Place the balls in the prepared baking dish. Cover with plastic wrap and let rise until doubled, about 45 minutes to 1 hour.
Preheat the oven to 375°F.
Uncover the rolls and bake for 22-24 minutes, or until deep golden brown (internal temperature should reach 190°F).
While the rolls bake, melt the 2 tablespoons butter for topping. Immediately after baking, brush the hot rolls with the melted butter and sprinkle evenly with the 1 teaspoon kosher salt. Serve warm.