我一字一字地学习汉语 OR 我一个字一个字地学习汉语 Which is the correct use of this grammar pattern?

我一字一字地学习汉语。

我一个字一个字地学习汉语。

The first one feels correct to me. The pattern is:

一{MW,N}一{MW,N} + 地 + V
Both are correct, but the second one sounds more natural to a native speaker.

个 is omitted only in some idiomatic phrases like 一字一句 or 一字排开(though here 一 doesn't mean the number, but the shape of the number).

In Chinese, it's more idiomatic to use a measure word between the number and the noun in most cases.