I do this, too... and have burned holes in the carpet with my stares! Things that help me:

T and me: Figuring out what part of me is protecting me from answering--Will my response bring shame? (Often the case.) Why was I conditioned to feel shame? Then she'll gently let me know that I have nothing to be ashamed of.

T: 1) Her asking questions, trying to draw out the answer with smaller less threatening questions. Sometimes she'll guess and she's wrong and I'll let her know and then allow myself to correct her. Sometimes it's like the game 20 questions... but it does often work.
2) After 5 or so minutes of small talk at the beginning of the session, she'll have me close my eyes and we do a meditation in which she talks to the scared/child parts and lets them know that her office is a safe place of non-judgment, that she welcomes and loves all parts of me, reminds me of the core in me that emanates out love for myself and others. Then we start to go into the deeper stuff. Sometimes the short meditation isn't enough and we might need to do another one.

Me: 1) Writing down an answer to a really tough question and then handing it to her to read (some Ts might make you read it).
2) After I leave I often deeply regret it if I can't get any of my answers out so I try hard to remember this as my stares start burning holes. Almost all the time I do eventually answer her questions, but sometimes with only 15 minutes left so I leave feeling very unsatisfied because we had to stop just when we started making progress.

Good luck! Remember, you've come this far and though it might be hard and frustrating, *this* is part of the process. With some gentle guidance you soon will allow yourself to talk