Place avocados in a blender or food processor. Add broth and the water; cover and blend or process until smooth. Add half-and-half, salt, onion powder, and white pepper. Cover and blend or process until combined.
Transfer avocado mixture to a glass bowl. Stir in lemon juice. Cover and chill for 3 to 24 hours. Stir before serving. If desired, garnish with lemon wedges and queso fresco.