The secret is to chill everything except the vermouth in the freezer before you start. To make a "filthy" martini, increase the olive juice by a few tablespoons.
Fill a cocktail shaker with crushed ice. Add vermouth; cover with lid, and shake until thoroughly chilled. Discard vermouth, reserving ice in shaker. Add vodka and Spanish olive brine to ice in shaker; cover with lid, and shake until thoroughly chilled (about 30 seconds). Pour into a chilled martini glass. Serve immediately with a large pimiento-stuffed Spanish olive.