In a large mixing bowl, whisk together 2 cups of all-purpose flour, 3/4 cup of granulated sugar, 2 teaspoons of baking powder, and 1/2 teaspoon of salt until thoroughly combined. In a separate bowl, blend 1 cup of sour cream, 1/4 cup of melted unsalted butter, 1 large egg, and 1 teaspoon of vanilla extract. Gradually add the wet mixture to the dry ingredients, mixing gently until a smooth dough forms.

On a lightly floured surface, roll the dough out to about 1/2-inch thickness. Using a donut cutter or two round cookie cutters of different sizes, cut out donut shapes, gently pressing down to create holes in the center. Place the shaped donuts onto a floured baking sheet.

In a large, deep pot or Dutch oven, pour in enough oil to submerge the donuts, about 2-3 inches deep. Heat the oil over medium heat until it reaches 350°F (175°C). To check readiness, drop a small piece of dough into the oil; it should sizzle and rise to the surface when hot enough.

Carefully add the donuts to the hot oil, frying them in small batches. Cook each side for about 1-2 minutes or until they turn a golden brown. Use a slotted spoon to flip them halfway through for even cooking. Once done, transfer the donuts to a wire rack lined with paper towels.

While the Sour Cream Donuts are still warm, dip them in glaze or dust them lightly with powdered sugar. Roll some in cinnamon sugar until coated.