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Preheat oven to 360°F/182°C. Line baking sheets with parchment paper.
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In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
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Pour melted butter into a large bowl and whisk in sugars until smooth. Add the egg, and whisking well until combined. Stir in vanilla. Add the flour mixture and mix, using a silicone spatula, until mostly blended. Stir in chocolate and keep mixing as little as possible, just until everything is blended.
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Roll dough into balls, each about the size of 2 tablespoons, and arrange them on the prepared pans, spacing them 3 inches apart. Sprinkle each cookie with a bit of coarse salt and bake for 10-12 minutes or until the tops are cracked and very lightly golden.
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Allow cookies to cool for a few minutes, then gently transfer cookies to a wire rack to cool completely.