Chop your peeled and cored pear into small cubes. It does not have to be perfect. Slice your vanilla bean pod in half width-wise.
In a small saucepan, stir together the chopped pear, sugar, lemon juice, and vanilla bean pod. Cook over medium-high heat for 5-10 minutes, or until the pears have softened.
Remove from the heat, and pull out your vanilla pod halves. Slice them in half length-wise and scrape out the seeds with the back of your knife. Stir into the pear mixture, along with the vanilla extract.
Transfer the mixture to a food processor or blender, and blend until completely smooth, about a minute. Transfer to a bowl and let cool.
Add the pear puree and vodka to a shaker with ice. Gently shake 2-3 times. Divide evenly between two cocktail glasses with ice. Top with the club soda, using more or less as needed. Add a slice of a pear or lemon peel for garnish, and enjoy!