Preheat and Prepare:

1. Preheat your oven to 350°F (175°C).
2. Grease a 9×13-inch baking pan with butter or nonstick spray.

2. Make the Batter:

1. In a large mixing bowl, combine the carrot cake mix, grated carrots, vegetable oil, milk, eggs, and cinnamon.
2. Mix until smooth and well combined.
3. Fold in chopped pecans or walnuts, if desired.

3. Prepare the Cinnamon Sugar Filling:

1. In a small bowl, mix together the brown sugar and cinnamon.

4. Assemble the Buns:

1. Pour half of the batter into the prepared baking pan and spread it evenly.
2. Sprinkle the cinnamon-sugar mixture evenly over the batter.
3. Pour the remaining batter on top, spreading gently to cover the cinnamon-sugar layer.

5. Bake:

1. Place the pan in the preheated oven and bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
2. Allow the cake to cool slightly in the pan on a wire rack.

6. Prepare the Glaze:

1. In a small bowl, whisk together powdered sugar, milk, and vanilla extract.
2. Adjust the consistency with extra powdered sugar or milk as needed.

7. Finish and Serve:

1. Pour the glaze evenly over the warm cake, letting it drip down the sides.
2. Garnish with extra chopped pecans if desired.
3. Slice and serve warm or at room temperature.