Add split pears to a medium saucepan with 2 cups water, champagne, sugar, and lemon peel. Bring to a simmer over medium-low heat and cook 30 minutes, or until just tender. Allow pears to cool in the liquid.
Meanwhile whisk together egg, yolks, salt, and lemon juice. Continue to whisk mixture while slowly drizzling in oil.
Place pears core-side-up on a plate. Put a dollop of egg mixture in each. Grate cheese on top. Serve.