Combine sweet potatoes and milk in a saucepan over medium heat. Bring to a simmer and cook for 15 to 20 minutes, until softened. Watch the mixture and if it starts to get too dry, add a glug of milk or water. By the end, almost everything will be evaporated but make sure there is a little liquid while cooking. Puree the mixture and place in a bowl to cool to room temperature.
In the bowl of a stand mixer, combine yeast, warm water and granulated sugar. Stir to dissolve then let sit for 10 minutes, until foamy.
Meanwhile, melt 4 tablespoons butter and allow to cool slightly. After the yeast is activated, add sweet potato puree, melted butter, salt and eggs. Mix until combined. Add flour, 1 cup at a time, until a soft ball of dough forms. It will be sticky.
Grease a large bowl with nonstick spray or olive oil. Add dough to bowl and flip to ensure it's all coated. Cover with a kitchen towel and place in a warm area to rise until doubled, about 1 1/2 to 2 hours.
Punch risen dough and let rest for 5 minutes. While dough is resting, grease two 9-inch cake pans. Divide dough into 16 equal sized balls. Roll and place evenly among each cake pan. I placed 7 around the edge of the pan and one in the middle. Cover with towel and rise until doubled, about 30 to 45 minutes. While they are rising, preheat oven to 375 degrees F.
Bake rolls for 12 to 18 minutes, until golden (mine took 15 minutes). While rolls are baking mix together the melted butter and honey. Brush the rolls with the honey butter as soon as they are done baking. Serve warm.