My T usually just asks "what do you need today?" or something similar. She used to ask "how are you doing" but I went on kind of a rant one time about how much I hate that question, so she almost never asks it as a conversation starter.

She has asked me near the end of a session, but then it really is to check and make sure I'm okay to leave her office.
Anyway, while my T prompts me by asking what I need, I usually have to start the conversation by picking the topic. There have been times where I just really don't know where to start, and I'll tell my T that. She'll usually start asking me questions about things we've talked about before, and eventually we both figure out what needs to be talked about. When I really don't know where to start, I just tell my T "I don't know what I need today. I have no idea where to even start. Can you please just prompt me with some questions?" She always prompts with relevant questions...asking about specific issues I've been dealing with.