**Preheat the Oven**

Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper for easy removal.

**Prepare the Zucchini**

Grate the zucchini using a box grater or food processor. Place the grated zucchini in a clean kitchen towel or cheesecloth, and squeeze out any excess moisture. Set aside.

**Mix the Dry Ingredients**

In a medium bowl, whisk together the flour, baking soda, cinnamon, and salt. Set aside.

**Make the Batter**

In a large bowl, cream together the softened butter and sugar using an electric mixer or whisk until light and fluffy, about 3-4 minutes. Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.

**Combine Wet and Dry Ingredients**

Gradually add the dry ingredients to the wet ingredients, alternating with the milk, and mix until just combined. Be careful not to overmix. Stir in the grated zucchini until evenly incorporated.

**Prepare the Cinnamon-Sugar Swirl**

In a small bowl, mix together the cinnamon and sugar for the swirl. Set aside.

**Assemble the Bread**

Pour half of the batter into the prepared loaf pan. Sprinkle half of the cinnamon-sugar mixture over the batter. Add the remaining batter on top and swirl the cinnamon-sugar mixture gently with a knife or skewer to create a marbled effect.

**Bake the Bread**

Bake the bread in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center comes out clean. If the bread starts to brown too quickly, cover it loosely with aluminum foil and continue baking.

**Cool and Serve**

Remove the bread from the oven and allow it to cool in the pan for 10 minutes. Transfer to a wire rack to cool completely before slicing.