Italy has reported record increases in the number of new coronavirus cases, increases

the likes of which we never saw here during the darkest days of pandemic earlier this year.

首先，increases在此为名词，而不是动词。increases the likes of which...为名词词组，是对前面的名词increases的补充说明（supplement补充语）。the likes of which...为限制性定语从句修饰increases. 名词likes在此意为the similar things。

句子翻译如下：

意大利报道了创纪录的新冠病毒感染人数的增加，类似的新增人数在今年年初病毒大流行最严重的时候都没有见过。