Line a small tray with parchment. Spoon or pipe 16 nickel-size coins of Nutella (about 1 generous teaspoon each) onto the tray and refrigerate until firm, 20–30 minutes.
Brown the butter: Melt the butter in a light-colored saucepan over medium heat, stirring, until the milk solids turn deep amber and it smells nutty, 5–7 minutes. Scrape into a large bowl and cool until just warm and slightly thickened, 10–15 minutes.
While the butter cools, whisk together the flour, cocoa powder, cornstarch, baking powder, salt, and espresso powder in a medium bowl.
Whisk the brown sugar and granulated sugar into the warm browned butter until glossy. Add the egg, egg yolk, and vanilla; whisk for 30–45 seconds until the mixture lightens slightly and looks emulsified.
Add the dry mixture and fold with a spatula just until no dry streaks remain. The dough will be soft. Cover and chill 15 minutes to make it easy to handle.
Preheat the oven to 360°F (182°C). Line two baking sheets with parchment paper.
Portion the dough into 16 even mounds (about 2 tablespoons each). Flatten one mound in your palm into a 2-inch round, place a firm Nutella coin in the center, and wrap the dough around it to seal. Roll into a smooth ball. Repeat with remaining dough, keeping any unused Nutella coins in the fridge as you work.
Roll the sides of each dough ball in the chopped toasted hazelnuts to coat the “equator,” leaving the top and bottom exposed for spread. Arrange 8 balls per sheet, spaced well apart.
Chill the tray of shaped cookies for 10 minutes while the oven finishes heating; this helps keep the centers thick and gooey.
Bake one sheet at a time for 10–12 minutes, until the edges are set and the tops look matte but the centers are still soft. If desired, tap the pan once on the rack to settle the crumb.
Immediately sprinkle each cookie with a pinch of flaky sea salt. Cool on the sheet for 8 minutes, then transfer to a wire rack to finish cooling. Serve warm for molten centers or at room temperature for fudgier middles.