Preheat oven to 360F or 182C. Line 2 baking sheets with parchment paper.
In a heavy bottomed saucepan over the lowest heat possible, melt butter, stirring occasionally. Don’t let the butter bubble or boil or else it will lose moisture.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
Pour melted butter into a large bowl and whisk in sugars until smooth. Add eggs, one at a time, whisking well until combined. Stir in vanilla. Add the flour mixture and mix, using a wooden spoon or silicone spatula, until mostly blended. Stir in chocolate and keep mixing as little as possible, just until everything is blended.
Roll dough into balls, each about the size of 3 tablespoons, and arrange them on the prepared pans, spacing them 3 inches apart. You can bake them right away or cover and refrigerate. Sprinkle each cookie with a bit of sea salt and bake until the tops are cracked and very lightly golden, 10-12 minutes. Allow to cool for a few minutes, then gently transfer cookies to a wire rack to cool completely.
Cookies can be kept at room temperature in an airtight container for up to 3 days. They also freeze well for up to 2 months.