Step 1: In a small bowl, combine warm milk and 1 tablespoon of the sugar. Sprinkle yeast over the top and let sit for 5-10 minutes until foamy.
Step 2: In a large mixing bowl or stand mixer, whisk together the sweet potato puree, remaining sugar, melted butter, and egg until smooth.
Step 3: Add the yeast mixture to the sweet potato mixture and stir to combine. Gradually add 3 cups of flour, the spices, and salt.
Step 4: Knead the dough for 5-7 minutes, adding more flour as needed until the dough is smooth and slightly tacky but not sticky.
Step 5: Place dough in a greased bowl, cover with a damp cloth, and let rise in a warm place for 1 to 1.5 hours until doubled in size.
Step 6: Roll out dough to 1/2 inch thickness on a floured surface. Cut into rounds using a doughnut cutter. Let the cut doughnuts rise again for 30 minutes.
Step 7: Heat 2 inches of oil in a heavy pot to 350°F. Fry doughnuts for 1-2 minutes per side until golden brown. Drain on paper towels and immediately toss in the cinnamon-sugar mixture.