Combine the milk and water in a small saucepan and heat until it reaches a temperature of 102°F-110°F.
Add 1 tsp of sugar, along with the yeast, to the milk/water mixture. Gently stir a few times and then set aside to proof for about 5 minutes.
Fit a stand mixer with a dough hook attachment. Add to the mixing bowl the 1/3 cup of sugar, flour, salt, rosemary, eggs, melted butter and mashed sweet potato.
Stir on low speed until all the ingredients are combined. It will be quite dry. You may need to scrape down the sides of the bowl to help ensure everything is well incorporated.
Add the yeast mixture and keep mixing on low speed until a smooth dough forms. You'll know its ready when the dough easily pulls away from the sides of the mixing bowl.
Take the dough and place it onto a lightly floured surface. Knead a few times until it becomes a smooth, uniform ball. Place in a large, lightly greased bowl. Cover, place in a warm location, and let rise for about 1 hour until the dough doubles in size.
Turn the risen dough out onto a lightly floured surface. Divide into 20 equal pieces. Shape each piece into a smooth, round ball and place in a lightly greased 9x13 baking dish, lined with parchment. Cover again and let rise for another hour.
Pre-heat your oven to 325°F. Bake the buns for 20-25 minutes until golden brown on top.