Preheat the oven to 350°F (180°C). Line two baking sheets with parchment paper.
Place the chopped dark chocolate and sunflower oil in a heatproof bowl. Set the bowl over a saucepan of gently simmering water, making sure the bottom of the bowl doesn’t touch the water. Stir occasionally until the chocolate is completely melted and smooth.
Remove the chocolate from the heat and let it cool for a few minutes. It should still be fluid, but not hot when you add it to the eggs.
Add the eggs and sugar to a large bowl. Whisk by hand for 1 to 2 minutes, until the mixture looks pale and slightly frothy.
Slowly pour the melted chocolate into the egg mixture while stirring. Continue mixing until everything is smooth and evenly combined.
Sift in the flour, cornstarch, and baking powder. Fold with a spatula until no dry flour remains and the batter looks thick and glossy.
Scoop small portions of batter onto the prepared baking sheets using a small cookie scoop or two spoons. Leave about 2 to 2½ inches (5 to 6 cm) between the cookies because they will spread as they bake.
Bake one tray at a time on the middle rack for 10 to 11 minutes, rotating the baking sheet halfway through.
The cookies are ready when cracks appear across the tops but the centers still look slightly soft. Don’t keep baking until they feel firm because they will continue to set as they cool.
Leave the cookies on the baking sheet for at least 30 minutes without moving them. Once they are firm enough to handle, carefully transfer them to a wire rack and let them cool completely.
Melt the white chocolate in a heatproof bowl over gently simmering water, stirring until smooth. Let it cool slightly, then transfer it to a piping bag and snip a very small opening at the tip.
Pipe uneven, overlapping lines of white chocolate across each cookie to make the mummy bandages. Add the candy eyes right away, before the white chocolate sets.
Leave the cookies at room temperature until the white chocolate is completely firm.