more often is correct.
No, you do not pronounce the t in often. I should edit this and say I don't pronounce the t, and I know many people that don't. But some people do. I don't know if that is confusing or not. Which is the correct way? I don't know, but both are accepted.
Okay, last edit, I checked the dictionary because I became curious about this and both ways are correct:
https://www.merriam-webster.com/dictionary/often
They don't pronounce the "t" in my region, but I think they do in upstate New York. Maybe. Any upstate New Yorkers here?