Cook + Dry the Sweet Potatoes: Peel and cut the sweet potato (1 medium) into ½-inch pieces. Rinse well, place in a saucepan, cover with water, and boil until fork-tender, about 10 minutes. Drain, then return to the warm pot and cook over low heat for 1–2 minutes to evaporate excess moisture. Mash until completely smooth. You should have about ½ cup (120 g). Cool to 80–85°F (27-29ºC). Activate the Yeast: In a small bowl, combine the warm 105°F (41ºC) water (1/4 cup), yeast (2 1/4 teaspoons), and sugar (1 tablespoon). Stir and let it sit 5–10 minutes, or until foamy and bubbly.
Combine the Wet Ingredients: In the bowl of a stand mixer, add the warm milk (1 cup) and cooled melted butter (1/4 cup). Stir in the activated yeast mixture, then add the cooled mashed sweet potatoes.
Start the Dough: Add 2 cups of the bread flour and mix with the paddle attachment until a soft, sticky dough forms.
Add Remaining Flour: Switch to the dough hook. Add the salt (1 1/2 teaspoons ) and 1/2 cup of flour. Continue adding flour ½ cup at a time until the dough cleans the bottom and sides of the bowl, feels tacky but not gluey, and begins to form a soft ball.
Knead the Dough: Knead on medium speed for 8–10 minutes, or until the dough is smooth, elastic, and can stretch toward a windowpane.
First Rise: Lightly grease a clean bowl with baking spray. Transfer the dough to the bowl, cover, and let rise for about 90 minutes, or until doubled in size.
Shape the Rolls: Grease a 9×13 baking dish (line with parchment if desired). Turn the dough out onto a clean surface and divide into 12 equal portions. Shape each into a tight ball and place them in the prepared pan. Cover and let rise for 30 minutes, or until puffy.
Preheat the Oven: About 20 minutes into the second rise, preheat the oven to 375°F. If using egg wash, whisk together the egg (1) and 2 tablespoons of water.
Bake: Brush the tops of the rolls with the egg wash if using. Bake for 17–22 minutes, or until the tops are golden brown. If your oven runs hot, start checking at 16 minutes.
Cool + Serve: Remove from the oven and cool for 10 minutes before separating the rolls. Brush with melted butter if desired.