Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add carrots and broccoli, cover, and steam until tender, about 20 minutes.
Transfer steamed carrots and broccoli to a blender or food processor. Add breast milk and water and blend until creamy. Strain mixture through a fine-mesh sieve to remove any lumps.
Spread blended mixture into an ice cube tray, cover with plastic wrap, and freeze until solid, 2 to 3 hours.
Transfer frozen cubes to a zip-top freezer bag and store in the freezer.