In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, salt, and ground cinnamon until well combined.

Add the softened butter to the dry ingredients and mix until the mixture resembles coarse crumbs.

In a separate bowl, whisk together the egg, whole milk, and vanilla extract. Pour this mixture into the dry ingredients and stir until just combined. Do not overmix; the dough should be slightly sticky.

Cover the bowl with plastic wrap and let the dough rest in the refrigerator for about 30 minutes.

In a deep skillet or heavy pot, heat about 2 inches of vegetable oil over medium heat until it reaches 350°F.

On a floured surface, roll out the dough to about 1/2-inch thick. Cut the dough into squares or rectangles, approximately 2 inches in size.

Carefully drop the dough pieces into the hot oil, a few at a time, and fry for about 2-3 minutes on each side, or until golden brown. Use a slotted spoon to remove them from the oil and drain on paper towels.

While still warm, dust the beignets generously with powdered sugar. Serve immediately.