Add all ingredients into an ice-filled cocktail shaker. Shake and strain into a double old fashioned glass filled with crushed ice. Garnish with lime wheel.
Measure granulated sugar into a large heavy-bottom saucepan. Pour in ¼ cup water. Do not stir. Measure out in a separate bowl remaining cup water and stir in brown sugar until dissolved. Set aside near the stove unit you will be using.
Place saucepan over medium-high heat and bring to a boil without stirring. Let bubble briskly for 4 to 5 minutes or until the sugar begins to change color. Without stirring, swirl pan gently on the unit until the color becomes deeply golden. Avert your face (as hot steam rises) and near the side rather than in the middle of the pan, pour in brown sugar mixture. Boil briskly for 5 minutes. Slide pan off heat and stir in butter, lemon juice and vanilla. The syrup is extremely hot so leave to cool in pan on stove until warm. Syrup thickens as it cools.
Recipe adapted from: Cate, Martin. "Daisy De Santiago." Smuggler's Cove: Exotic Cocktails, Rum, and the Cult of Tiki." Bereley: 10 Speed Press, 2006. p. 171.