Begin by preheating your oven to 250°F (120C/100C Fan) and line a large baking sheet with a piece of parchment paper or a silicone mat.
Place the egg whites, caster sugar and brown sugar in a heatproof bowl (ideally, the bowl for an electric mixer, fitted with a whisk attachment).
Use a small, deep-sided saucepan, that you are able to set the mixing bowl over without it sitting in too deep and touching the bottom. Pour about an inch of water into the pan and bring this to a simmer. Place the mixing bowl on top of the saucepan (it should not touch the water). Keep the water simmering while you whisk the egg whites and sugar by hand continuously until these are frothy and the sugar melted.
Remove the mixing bowl from the saucepan and fit this back in the electric stand mixer, fitted with a whisk attachment. Whisk the egg whites and sugar on a high speed until these are cool, thick and glossy (about 5-7 minutes).
When ready, spoon the meringue out onto the prepared baking sheet and spread into a circle about 9" or 23cm in diameter. Create a bit of a nest by pushing the meringue to the edges, allowing these to be slightly taller than the centre.
Place this in the centre of your preheated oven and bake for three hours. At the end of the three hours, turn the oven off and allow to cool completely in the oven (usually around 2 or 3 hours depending on your oven).
When your meringue is just about ready to be removed from the oven at the end of the cooling, melt your white chocolate in a small bowl set over a pan of simmering water. Spread this gently over the central nest of the meringue and set aside to cool at room temperature until set (usually about 2 or leave overnight).