Is it acceptable to omit 的 before a noun in degree complement, when the verb follows the noun?
You cannot omit the possessive 的 in 你的菜, 你的字, 你的中文, if your comments are about 'your cooking', 'your writing' or 'your Chinese'

However, you can remove (not omit) '的' to change the topic from '你的~ (your~)' to '你 (you)'


  [你的菜 (topic)] [做得很好(comment)] - "your cooking is cooked very well" 
  
  [你的字 (topic)] [写得很漂亮 (comment)] " your writing is written very beautifully"
  
  [你的中文 (topic)] [说得很好 (comment)] "Your Chinese is spoken very well"
  
  '你的菜', '你的字' and '你的中文' are the topics


~


  [你 (topic)] [菜做得很好 (comment)] - "you cook very well"
  
  [你 (topic)] [字写得很漂亮 (comment)] - "you write very beautifully"
  
  [你 (topic)] [中文说得很好 (comment)] - "you speak Chinese very well"
  
  '你' is the topics


~ 


  '你做得很好', '你写得很漂亮' and '你说得很好' are basic [subject + verb]  phrases