I believe the biopsy description of "small basophillic cells forming tumor islands" is describing the peripheral palisading that is classically seen in Basal cell carcinoma.

All other types are either pigmented or have scales. -- process of elimination

'round, semitransparent nodules'

FA2019 p.473 says BCCs are waxy, pink, pearly nodules

Basal cell carcinoma is characterized by nests of basal cells (tumor islands), surrounded by clear spaces (clefting, the white artifact) and extends across the BM (carcinoma)

http://www.pathologyoutlines.com/topic/skintumornonmelanocyticbcc.html

Anything upper lip + above → basal cell carcinoma

Anything lower lip → Squamous cell carcinoma

FA 2019 -pg 473