1. Make the caramel syrup: In a small saucepan, bring the sugar, water, allspice and cinnamon to a boil over high heat, stirring occasionally to dissolve the sugar. Reduce the heat to medium and continue to cook, stirring occasionally, until the mixture reaches 380°, 12 to 14 minutes. At this point it will turn deep brown quickly, so keep an eye on it, swirling the pan often, until the mixture is deep brown, 1 to 2 minutes longer. Turn off the heat and immediately add the boiling water to prevent the syrup from solidifying. Set aside.

2. Make the cola: In a small saucepan, bring the kola nuts and water to a simmer over medium-high heat. Reduce heat to medium and simmer for 15 minutes.

3. Meanwhile, in a medium bowl, use your fingers to rub the lime zest into 2 tablespoons of the sugar to extract the oils from the citrus zest. Add the lime-sugar mixture to the kola nuts along with the cooled caramel syrup, lime juice, citric acid, vanilla and the remaining sugar, stirring until sugar is dissolved.

4. Simmer another 10 minutes, take off the heat and cool completely. Line a sieve with a doubled layer of cheesecloth and set over an airtight container, then strain the cooled cola mixture through the cheesecloth. Refrigerate for up to a month. To serve, mix 1/4 cup (2 ounces) of the cola with the soda water.