Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan well.
In a small bowl, stir together 1 cup brown sugar and the cinnamon to make the swirl filling. Set aside.
In a medium mixing bowl, whisk together the flour, baking powder, salt, and 1/3 cup brown sugar.
In another bowl, whisk the egg, milk, melted butter, vanilla extract, and sourdough discard until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Do not overmix.
Spread half of the batter into the prepared loaf pan.
Sprinkle about three-fourths of the cinnamon-sugar mixture over the batter.
Add the remaining batter on top, then finish with the rest of the cinnamon-sugar mixture.
Use a knife to gently swirl the layers for a marbled effect.
Bake the Sourdough Discard Cinnamon Bread for 45 to 50 minutes, or until a toothpick inserted in the center comes out clean.
Let the loaf cool in the pan for about 20 minutes, then transfer to a wire rack to cool completely before slicing.