In a shallow pan, combine 1/3 cup sugar and the cinnamon; set aside.
In a medium-sized bowl, using an electric mixer, cream together the butter and remaining 1/3 cup sugar until creamy. Add the eggs and vanilla, blending well. Mix in 1 cup of the flour, the baking powder, and salt; mix well and blend in the milk. Add the remaining flour and mix to make a soft dough.
Turn out onto a floured surface and knead for 1 to 2 minutes or until the dough is smooth, kneading in more flour if the dough is still too sticky to handle. With a rolling pin, roll out dough to 1/4-inch thickness, flouring the surface and rolling pin lightly if the dough sticks. Cut the dough with a 2-inch round cookie cutter.
In a heavy skillet or Dutch oven, heat 2 inches of oil over medium heat, until hot but not burning or smoking (350 degrees). Fry six 2-inch rounds at a time for 1-1/2 to 2 minutes, until puffy and golden, turning often with tongs. Drain on paper towels and toss in the sugar and cinnamon coating mix while still hot.