Preheat oven to 400°F. Lightly butter an 8x8-inch heavy baking dish.

Add the semi-sweet chocolate chips to a heatproof bowl. Pour the warmed heavy cream over the chocolate and let sit for 1–2 minutes. Whisk until smooth and glossy. Add the butter and kosher salt and whisk until completely melted and smooth. Pour the ganache into the prepared baking dish and spread into an even layer.

Add the melted butter, granulated sugar, cocoa powder, and espresso powder to a saucepan over medium-low heat. Whisk for 1–2 minutes, until smooth and glossy and the sugar has started to dissolve. Do not bring to a boil. Remove from the heat and stir in the vanilla bean paste and salt.

Place the egg yolks in a small bowl and whisk until smooth. Slowly add about ¼ cup of the warm chocolate mixture to the yolks, one tablespoon at a time, whisking constantly. Once tempered, slowly whisk the egg mixture back into the remaining chocolate mixture until smooth.

Add the flour to the chocolate mixture and stir just until no dry streaks remain. Fold in the chopped dark chocolate. The batter will be thick and fudgy.

Spoon the chocolate batter evenly over the ganache layer, being careful not to disturb the ganache underneath too much.

Bake at 400°F for 22–27 minutes, checking around 22 minutes. The edges should be set and the top should look baked. Do not overbake.

Remove from the oven and let rest for 5–10 minutes. Scoop the warm cobbler into bowls and serve with vanilla ice cream and flaky sea salt.