I playfully fake stuttered in front of my parter that stutters while we were flirting and I made the biggest mistake of my life

I playfully fake stuttered in front of my parter that stutters while we were flirting and I made the biggest mistake of my life Hi, I'm writing here because I want to better myself and want to acknowledge the mistake that I've made and for whom I genuinely feel disgusted and terribly sorry. I'm honestly so disappointed and wish to know more and how to fix this, even if I've excused myself. My partner and I were being flirty, I had sent them a hot photo, they don't always stutter because they have learned how to control but when they feel emotional they start stuttering. My partner, after having viewed the pic, said something stuttering, which I repeated after, stuttering, in a flirty tone. In my head, their stuttering was totally disconnected from the fact that they stutter and I wanted to joke about how the pic made them stutter, not in the sense that they are a stutterer, but in the sense of "wow this pic left me speechless" kind of romantic trope. I honestly hadn't taken into consideration their stutter problem and I was honestly being playful about it, without any bad apparent intention behind it. This is not the first time they've stuttered around me, it has happened multiple times and I don't see a problem in it and I've always said that they can stutter how much they want around me since they will not get judged. They were bullied for their stutter problem and even an ex-partner of theirs made fun of their stutter during an argument, which is truly horrible. After the incident I excused myself, I know that I should have never, even if it wasn't with bad intentions, done that. I know and I'm deeply sorry. They told me they felt hurt, blessed, and disappointed by my behavior. I honestly feel like the worst person on planet earth, I didn't want to disappoint them and I would like to better myself. I even proposed them to break up with me if they don’t feel comfortable anymore being with me and being with somebody that was so insensitive about this. What can I do for my partner and how can I make them feel better? I'm truly deeply sorry of the incident and I should have never been this insensitive.