Frog and Toad are not at all alike. Frog likes new adventures. Toad likes the comforts of home. Yet despite their differences, Frog and Toad are always there for each other—as best friends should be.

While some bosses spend their final months on a job easing into retirement and smoothing their successor’s path, Brosius is directing up a storm during the last of his 27 seasons as artistic director ...