In a small saucepan bring water to boiling. Add carrots; cover and cook for 10 to 15 minutes or until very tender, adding ginger slices for the last 2 minutes of cooking. Remove from the heat and add tea bags. Cover and steep for 4 minutes.
Remove tea bags, squeezing out all the tea. Remove ginger slices. Set pan on a hot pad in the refrigerator for 10 minutes. Transfer carrot mixture to a blender. Add mango, honey, and chia (if using). Cover and blend until smooth. Pour into glasses to serve.