Garlic bread

Garlic bread is the sole connection between Sensei and the Upside Down House. It also acts as a key factor in connecting the current Sensei with an older versions (presumably Sensei Prime).

Sensei's Taste
At lunch with Ayane and Sana, Sensei expresses that he loves garlic bread so much that he would be satisfied if it was the only food he ever ate. Much later, Ami recounts memories from before Current Sensei took over in Kumon-mi where this past incarnation appeared to be severely depressed. He sat around in his bedroom all day, allowing trash to pile up and survived off of nothing but garlic bread and water. While there are numerous hints that the Current Sensei shares memories with one of his past selves, the garlic bread connection is one of the clearest examples of Current Sensei's personal preferences being shared by a previous incarnation.

The theory is that the memories Ami are recounting are actually from Sensei Prime, wallowing in sadness either after the car accident or after Maya's attempted suicide. The memories of that awful time period would have become so ingrained that they would have been passed onto Ami (and necessarily altered to include her fake past), and in addition would have informed Current Sensei's seeming obsession with the food.

The Upside Down House
At one point Sensei is viewing a TV program clearly linked to the Upside Down House in which a number of girls are idly eating garlic bread off of a paper plate in a small kitchen. Assuming that this is some sort of memory or video feed from the past, it creates a clear link between Sensei Prime and the Upside Down House. Presumably garlic bread became Sensei's comfort food during difficult times and as a result he wound up feeding it to the girls occupying (or trapped within) the facility. In addition to the Sensei link it also speaks to the poor conditions and likely mistreatment of the girls, and possibly the bootstrapped and poorly funded nature of the facility.