Use the wedge of lemon to wipe around the inside of the bowl of a stand mixer. Do the same for the whisk attachment. If using a hand whisk, do the same, making sure there is no grease or residue on either the bowl or whisks.
Add the chilled aquafaba and cream of tartar. Whisk on full speed until very foamy. Add the 1 tbsp caster sugar and whisk until stiff peaks form and the mixture is white and glossy - this can take up to 10-15 minutes, depending on your stand mixer and aquafaba. Stop the mixer when you're happy with the consistency.
Fill the sink or a large bowl with cold water.
Combine the remaining 150g caster sugar and the water in a small saucepan. Place over medium/low heat and stir to combine. Stop stirring at this point and just swirl the pan around occasionally if necessary.
Bring the sugar syrup to 115c/240f using a chef's thermometer to check. See notes above if you don't have a chef's thermometer. Remove from the heat immediately.
Turn the stand mixer to medium speed and, while the aquafaba mixture is being whisked, pour the sugar syrup into the bowl in a slow, thin drizzle. Once all the sugar syrup is added, with the whisk still running, slowly add the xanthan gum, little by little.
Stop the mixer and remove the bowl of marshmallow fluff. Submerge the base of the bowl in the sink of cold water and whisk the mixture by hand for around 3-5 minutes until it cools. You should notice the mixture thickening slightly as it cools.
Once cooled and thickened, spoon the mixture onto the cooled sweet potato cake. Use a chef's blowtorch to toast the topping. Alternatively, heat your grill/broiler to full power ad place the topped cake underneath until gently browned (careful - it can burn very quickly!)
Slice and serve immediately or cover and store in the refrigerator for up to 2 days.