I happen to quite like monotonous voices. But if you really want to change it, it seems like imitating other people is the key.
I have always been quite expressive, and I think it has a lot to do with me going to theater school/being a child actor when I was a kid. I always had a director who told me how to look, and how to say things.
I also used to imitate characters from movies. I could remember big chunks of dialogue and repeated it often, in the same way the characters did.
So, I guess studying and mimicking actors and practice in front of a mirror could be a good way. Or maybe even take an acting class, if it's not too uncomfortable.
I'm afraid it's going to feel very fake and stupid, and it won't come naturally for a very long time, if ever.
I was really lucky to get so much training from such a young age, so all expressions and tones of voice is a habit now. But I am still always conscious of how I'm acting, and still feel very fake sometimes. But I can't deny how useful it is to be able to pass for NT when it's needed.