Place citrus peels and sugar in a jar and let sit overnight to create an mixture of sugar and citrus oil. Or, one can do this more quickly by muddling peels and sugar together then allowing it to sit for 30 minutes.
Empty content of sugar mixture jar into punch bowl and add lemon juice, water, tea and vodka. Blend gently. Fill bowl with cubed ice and stir to chill. Grate a small amount of nutmeg over the top and float slices of lemon and orange in punch.