I can't even read Italian, let alone write it.

Literal

I [topic-は] Italian [object-を] write [nominalizer-の-は] foolish-not-to-mention, read-even cannot.

The はおろか pattern is the standard 'let alone, not to mention' construction. The clause before は names the more demanding thing (writing); the clause after states that even the easier thing (reading) is impossible. The おろか derives from 愚か ('foolish') frozen into a grammar pattern — 'foolish [to suggest], not to mention.' The 読めもしない uses も to layer 'even reading' onto the negation.