Billedbogen (The Picture Book) is a series of miniatures by the Danish composer Fini Henriques. It is noted for its Nordic lyricism and simple, heartfelt melodic writing.
The primary challenge is shaping the phrases with appropriate rubato without losing the steady underlying pulse.
Comparable difficulty and character — good candidates for what to learn next.
Billedbogen 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 Billedbogen lasts about 4 minutes.
Billedbogen 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 Berceuse by Fini Henriques, Believe Me, If All those Endearing Young Charms by Irish Folk Music, Valse sentimentale, No. 6 by Pyotr Tchaikovsky — see the full similar-pieces list on this page.