Line two baking sheets with parchment and preheat the oven to 350°F (177°C).
Make the chocolate center: Warm the cream in a small saucepan over medium heat just until steaming. Pour it over the chocolate chips in a heatproof bowl, cover, and let sit for 2 minutes. Stir until smooth and glossy, then set aside to thicken slightly while you prepare the cookies.
Whisk the flour, baking powder, baking soda, and sea salt together in a medium bowl.
In a large bowl with a hand mixer (or stand mixer), beat the softened butter and brown sugar on medium speed until light and fluffy, about 2 minutes. Beat in the egg and vanilla until fully combined, 30 seconds more.
Add the dry ingredients to the butter mixture and mix on low just until a soft dough forms with no dry spots. Cover and chill the bowl for 15 minutes to help the cookies hold their shape.
Scoop 1-tablespoon portions of dough (about 1-inch balls). Roll smooth and arrange 2 inches apart on the prepared baking sheets.
Press a deep well in the center of each ball using your thumb or the back of a 1/2-teaspoon measuring spoon. Tip: Warm the spoon in hot water, dry it, and then press—this helps prevent cracking around the edges.
Bake until the edges look set and just starting to turn golden, 9–10 minutes. If the centers puff, re-press the wells immediately after removing from the oven. Cool on the sheet for 5 minutes, then transfer to a rack to cool slightly.
Stir the ganache again; it should be thick but spoonable. Spoon or pipe about 1 teaspoon into each indentation. Let the chocolate set for 20–30 minutes, or enjoy while the centers are still a bit warm and glossy.