Preheat your oven to 365 F (185 C).
Start by making the cookie dough for the base. Combine your melted butter, sugar, egg, and vanilla extract in a medium mixing bowl. Separately, add your dry ingredients (flour, baking powder, and a pinch of salt) to a bowl and mix to combine.
Add your dry ingredients to your wet and combine until you have a cohesive dough.
Generously flour a surface and begin rolling out your dough. If the dough is very unmanageable/wet, you can refrigerate it for 15-30 minutes. You can also add more flour to the dough. You are aiming for about 1/8 inch thickness as you want the cookies fairly thin. Once rolled out, use a cookie cutter or the edge of a glass to cut out circles (our were about 2 inches in diameter).
Place on a baking sheet lined with parchment paper and bake for 8-10 minutes until lightly golden around the edges.
Note: you may have extra cookies leftover at the end of the process - something to snack on!
Let the cookies cool completely. Start your meringue mixture by adding your sugar and your water to a small saucepan. It should resemble wet sand.
Separate the egg whites from the yolks and add the whites to the bowl of a stand mixer. Add a splash of lemon juice. Start whipping on medium speed until foamy and about doubled in size. Add in the vanilla extract and mix briefly to combine.
Meanwhile, heat the sugar and water over medium heat without stirring until all the sugar has dissolved. You will need a thermometer to check the temperature of the mixture for the next stage. Once your sugar hits 230 F (110 C) to 235 F (112 C), restart your stand mixer on medium to low speed and slowly pour in your sugar mixture while the mixer is running. Your meringue should start to turn glossy almost immediately.
Stop the mixer when your meringue has reached stiff peaks.
Pipe or spread your meringue onto your cooled cookie bases. We found that adding the mixture with a knife works perfectly well! Just be sure to smooth it out as much as possible, so that your final product doesn't look too misshapen!
Once you have covered all of your cookies or run out of the marshmallow mixture, set your domes aside at room temperature to dry out for about an hour. This helps form a bit of a barrier so that the chocolate doesn't disintegrate the meringue.
Now you are ready to temper your chocolate! The process can be difficult - we found great directions and advice on this Sugar Geek Show post. If tempering chocolate is too daunting, no worries - just make sure to store your domes in the fridge to prevent them from melting at room temperature. We chose to use the seeding method for our chocolate tempering process and followed the directions on the Sugar Geek Show post, briefly summarized here: melt about 2/3 of your chocolate in a double boiler while stirring constantly, making sure to not exceed 110-115 degrees F. Then remove from the heat and add seed chocolate and continuously stir until the chocolate hits about 86-87 degrees F. The chocolate should be in temper if it sets quickly at room temperature, has a snap, and a glossy sheen. You can test this by spreading a small amount of chocolate on a piece of parchment paper and checking on it after a few minutes. If the first test doesn't set, you can wait a little bit and try again. Don't worry if it doesn't work out - you can always keep these in the fridge and they will still taste amazing!
Work quickly to coat your meringue domes once the chocolate is tempered. You may have to make a second batch of chocolate or reheat your first batch gently if it starts to set up too quickly. Optionally, you can add shredded coconut to some of the domes before they are fully set.
Let your domes set (at room temp if using tempered chocolate, in the fridge if not) and once the shell has hardened, enjoy!