This is a sentimental character piece by a minor Italian composer. Its charm lies in its simple, song-like melody and typical Italian operatic influence.
Focus on maintaining a smooth, singing tone in the right hand over a gentle, steady accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse di un ricordo is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 4.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Berceuse di un ricordo lasts about 3 minutes.
Berceuse di un ricordo is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include An imaginary cadence by Giuseppe D'Amico, Berceuse by Rudolf Friml, 'O marenariello by Salvatore Gambardella — see the full similar-pieces list on this page.