My intention is indeed to improve conversations with people I know well or semi-well. Some good questions with built-in blanks in this context are "How is your project X going?" or "What did you think of book X?". Do you have examples of other such questions? I think the kinds of questions you would use for starting a new topic and for deepening an existing topic are likely to be different, and the latter are much more context-dependent.

It does not seem difficult to avoid being robotic/unfun with these questions, if you ask them with actual caring and curiosity, and if the motivation is not to fill silence but to learn about the other person.