Line a large baking sheet with baking parchment. Using an 18cm round cake tin or plate as a guide, draw a circle on the parchment, then flip it over. Heat the oven to 130C/110C fan/gas ½.
Rub the reserved lemon half around the inside of a large bowl or stand mixer, then wipe with kitchen paper to remove any butter or oil. Tip in the egg whites and whisk with an electric whisk or the mixer on a low speed until the whites form small, foamy bubbles, about 1-2 mins. Keep going until the mix looks like shaving foam, then add the sugar, 1 tbsp at a time, until it’s a thick, glossy meringue. Rub some between your fingers – if you can feel any grains of sugar, keep whisking for a few minutes. Add the cornflour, lemon juice and vanilla, and whisk for another 30 seconds.
Spoon the meringue onto the prepared baking sheet, into the centre of the circle, and spread it out to the edges with a palette knife. Swipe the knife around the edge, then smooth the top.
Bake for 15 mins, then turn the oven down to 100C/80C fan/gas ¼ and bake for 1 hr. Turn the oven off and leave the pavlova inside to cool for at least 2 hrs, or overnight.
Carefully invert the pavlova and peel away the parchment. Don’t worry if it cracks a little – it will be covered by the topping.
To make the topping, blitz the mint with the caster sugar. Whisk the double cream and natural yogurt with an electric whisk until just holding its shape. Sprinkle over the lime zest and mint sugar, then fold into the cream mix with a large metal spoon to ripple. Spoon over the pavlova. Top with the rest of the mint sugar, the watermelon and more mint. Serve with lime wedges to squeeze over. Best served straightaway but leftovers will keep in the fridge for two days.