Make the vanilla simple syrup: Add the sugar to a small bowl. Use a paring knife to split the Private Selection® Madagascar Vanilla Bean lengthwise, then scrape out the seeds. Add the vanilla bean seeds to the sugar and use your fingers to combine.
Add the vanilla sugar, scraped vanilla bean, and water to a small saucepan. Bring to a boil over medium-high heat, then reduce the heat to low and simmer, stirring occasionally, until the sugar has dissolved. Remove the pot from the heat and let the syrup cool to room temperature before transferring to an airtight container with a lid. The syrup will keep in the refrigerator for up to 1 month.
Make the London fog: In a large pitcher, combine the gin, 2–3 tablespoons vanilla simple syrup, the Private Selection® Cold Brew Blueberry Lavender Black Tea, and oat milk. Add more simple syrup to taste, if needed.
Fill 4 glasses with ice and divide the London fog evenly between the glasses. Garnish each glass with a lemon slice and a lavender sprig. Serve immediately.