Fill your shaker 3/4 full with ice cubes. Cut the sides off of your lemons until you have 5 large chunks of peel with a little bit of the lemon still attached to them.
Squeeze the lemon peel into the shaker, then pour in the 4 ounces of vodka and the 2 ounces of dry vermouth. Seal the shaker, wrap a towel or cloth around it so it doesn't freeze your hand off, and shake until you can't shake anymore.
Strain twice, and pour into 2 cold martini glasses with 3 lemon twists inside each.
Notes
If you have a small shaker, you might have to do one cocktail at a time; mine just barely held all of this for 2 drinks.