Prepare the oven. Preheat the oven to 355°F and line two large baking sheets with parchment paper. Have all the ingredients measured before you begin.
Melt the chocolate. Place the chopped dark chocolate and sunflower oil in a heatproof bowl set over a saucepan of barely simmering water. Stir occasionally until the chocolate has completely melted and the mixture is smooth. Remove from the heat.
Dissolve the sugar. Add the caster sugar and water to a small saucepan. Heat over medium-low heat, stirring until the sugar has completely dissolved and the liquid no longer looks grainy. Do not let it caramelize.
Combine the warm mixtures. Pour the warm sugar syrup into the melted chocolate and whisk until the mixture is smooth and glossy.
Combine the dry ingredients. In a separate bowl, whisk together the all-purpose flour, cocoa powder, baking powder, salt, and instant espresso powder.
Make the batter. Add the dry ingredients to the warm chocolate mixture and whisk just until evenly combined with no visible pockets of flour or cocoa. The batter should be thick and glossy but softer than traditional cookie dough.
Portion the cookies. Scoop about 2 tablespoons of batter per cookie onto the prepared baking sheets to make 16 cookies. Leave about 2 inches between each cookie to allow for spreading.
Bake. Bake for 9–10 minutes, until the cookies have spread and puffed slightly and the tops look thin and crackled. The edges should appear set while the centers remain soft.
Reshape if needed. Immediately after baking, gently nudge any uneven edges into a round shape while the cookies are still hot and pliable.
Cool. Leave the cookies on the baking sheets for 5–10 minutes so the centers can finish setting. Once firm enough to move without breaking, carefully transfer them to a wire cooling rack.
