i don't really understand some parts (that i've bolded) of this tweet:

どうしてブルブルになって持ち直せなくなってしまったと言いますと、夕方、友達の事務所による用事があったので、豆花屋さんを見つけたのでそこで手土産を買いまして

冷たい方を頼んだら中にかき氷みたいなみぞれがいっぱいはいっていまして

でも美味しくて、シャクシャクとたべているうちに以下略

what is the reading/meaning of the 方 and 中 used here? and what is the whole line saying? my understanding is that she was buying a 手土産 at a 豆花屋 to bring to her friend's office and while she was requesting something cold, she noticed something that looked like shaved ice...? if so, why does that line end with はいっていまして instead of something like はいっている食べ物が気づいて? it feels like an incomplete sentence. also, i don't know how that logically/contextually leads to でも (she bought it, but it was delicious? huh?), which makes me think that i'm completely missing the meaning. lastly, うちに以下略 is completely lost on me.