talking to a shy boy i like who stutters

talking to a shy boy i like who stutters i am very attracted to a friends friend who stutters. i dont know him very well and i only see him when we hang out as a group and the last time we hung out i noticed that he was more relaxed than usual and we talked much more that we ever did, so i guess that he feels good around me. I am only guessing and relying on things our mutual friend told me about him - apparently he talksmuch more around people who he likes. he i am really interested in him, but he is quite quiet and shy and i am unsure on how i should approach him, i am the exact opposite - i talk a lot, i like telling jokes and silly stories that make people laugh. i really want to talk to him more and get to know him - he is really interesting, smart and i just feel a strong attraction to him. were both in out early twenties, he is a few years older than me. Ive googled tips on talking with someone who stutters, watched some helpful videos etc. but everything seems quite banal - finishing other peoples sentences, breaking eye contact and interrupting is just rude and ive never done that. can someone give me advice on how to approach him and let him know that i would very much like to spend some time with him - just the two of us without overwhelming and scaring him off? he has never had a girlfriend and has asmall but great friend group.