A new and distinct cultivar of Hydrangea plant named ‘SCHROLL42-12-01’, characterized by its compact, upright and mounded plant habit; moderately vigorous to vigorous growth habit; freely branching habit and strong stems; dark green-colored leaves; large mophead-type inflorescences with white-colored sterile flowers with red purple-colored margins; long flowering period; and good postproduction quality and longevity.