Preheat oven to 350°F (175°C). Grease a 9x5-inch loaf pan.
In a small bowl, mix 1/3 cup sugar and 2 teaspoons cinnamon. Set aside.
In a large bowl, whisk together flour, 1 cup sugar, baking powder, and salt.
Add milk, oil, eggs, and vanilla to the dry ingredients. Mix until combined.
Pour half the batter into the prepared loaf pan. Sprinkle half of the cinnamon sugar mixture over the batter.
Add the remaining batter and sprinkle the rest of the cinnamon sugar on top.
Use a knife to gently swirl the cinnamon sugar through the batter.
Bake for 50-60 minutes, or until a toothpick inserted in the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.