Use a slotted spoon to remove olives from the brine and place them on a plate.
In a medium mixing bowl, combine blue cheese and 1 tablespoon of heavy cream with an electric mixer until it is a spreadable consistency. Add more cream a tablespoon at a time if needed.
Use a pastry bag or a zip-top bag with a cut corner to fill the cavity of each olive with the creamy blue cheese mixture.
If serving as an appetizer, drizzle with olive oil and toss to coat. Place on a serving platter or in a bowl. Serve with toothpicks, tongs or olive forks.
If serving in cocktails, spear with cocktail skewers.
Stuffed olives are best enjoyed within a couple of days as an appetizer. For cocktails, enjoy within a week.