Exercise to the reader: How do you slice the bagel so that you can spread cream cheese continuously along both sides. In other words, can you make a Möbious bagel?
To think about it another way, imagine if you took a mobius strip and constructed a semicircular lump of bread on the surface, extending it around until it connects back to itself. You've made a bagel!
Now take the mobius strip out of the middle, and the gap it leaves is the cut you're asking to make.
I wonder if I could sell bagel-sized silicone mobius strips for baking.
I'd suggest raising a few million in seed funding and renting an office in downtown SF. If it doesn't pan out you can pivot into math-related silicone ice cube trays.