Prick sweet potatoes all over using a fork; place on a microwavable plate. Microwave on high, turning every 4 minutes, until softened, 8 to 12 minutes total. Let cool 10 minutes. Peel and discard skins. Mash sweet potatoes in a medium bowl using a fork until mostly smooth. Cook milk, 3 tablespoons sugar, and 3 tablespoons butter in a small saucepan over medium-low, stirring often, until sugar just dissolves, about 5 minutes. Let cool slightly, about 5 minutes. Meanwhile, stir together 1/4 cup warm water, yeast, and remaining 1 teaspoon sugar in a small bowl. Let stand at room temperature until foamy, about 5 minutes. Place milk mixture, yeast mixture, 1 cup (8 ounces) mashed sweet potatoes (reserve remaining sweet potatoes for another use), and 1 egg in bowl of a stand mixer fitted with a dough hook attachment. Beat on low speed until combined, about 30 seconds. Increase mixer speed to medium-low; gradually add flour and salt, beating until combined, about 1 minute. Increase mixer speed to medium; beat until dough is smooth, elastic, and slightly sticky, 6 to 8 minutes. (Dough should stick to bottom of bowl but pull away from sides.) Transfer dough to a large bowl lightly greased with cooking spray. Cover with plastic wrap. Let stand at room temperature until almost doubled in volume, 45 minutes to 1 hour. Turn out dough onto a lightly floured work surface, and divide into 30 (about 1-ounce) pieces. Shape into balls. Arrange dough balls in 6 rows of 5 balls each on a rimmed 13- x 9-inch baking sheet lightly greased with cooking spray, spacing about ½ inch apart. Cover loosely with plastic wrap. Let stand at room temperature until dough balls have almost doubled in size, 30 minutes to 1 hour. Meanwhile, preheat oven to 375°F. Whisk remaining egg in a small bowl until lightly beaten. Uncover rolls; brush lightly with beaten egg. Sprinkle rolls evenly with ajowan seeds. Bake in preheated oven until golden brown and puffy, 14 to 18 minutes. Brush hot rolls with remaining 2 tablespoons butter. Serve rolls warm, or transfer to a wire rack, and let cool completely, about 1 hour.