Preheat the oven to 350°F and grease a 9x5 loaf pan with cooking spray, shortening, or oil.
In a small bowl, stir together 1/3 cup sugar and the cinnamon until evenly combined. Set aside.
In a large bowl, whisk together the flour, 1 cup sugar, baking powder, and salt. Measure the flour using the dip-level-pour method so it isn't packed into the cup. Whisking the dry ingredients first breaks up any lumps in the flour.
Add the milk, vegetable oil, and vanilla to the dry ingredients.
Beat the egg in a separate small bowl, then add it to the batter. Beating it first helps it blend in evenly.
Stir with a spoon or spatula until the batter is smooth.
Pour a little less than half the batter into the prepared loaf pan and spread to cover the bottom.
Sprinkle most of the cinnamon sugar mixture over the batter, reserving about 2 teaspoons to 1 tablespoon for the top.
Pour the remaining batter over the cinnamon sugar layer and smooth the surface.
Lightly sprinkle the reserved cinnamon sugar over the top. Use a light hand — too much will sit on the surface instead of soaking into the bread.
Bake for 45 to 50 minutes. Ovens vary, so begin checking at 45 minutes.
Cool in the pan for at least 10 minutes. Run a knife gently around the edges to loosen, then turn the loaf out and cool completely before slicing.