I'd be convinced that he was just a look a like as l walking down my 街, 街道 would be TOO much of a miracle for me. Though I'd watch him and see which house he goes in.
Hmm..In that situation I would probably check if it's dream-if it wasn't then I would get nervous and if he was coming my way..I would say Hi..and that's it XD
Casually follow him to his house and when I see where he lives, make a bajillion desserts and randomly leave them on his doorstep. Then he will marry me.