Heat the oven to 175 C / 350 F. Line a 9x13-inch (23x33 cm) baking pan with parchment, leaving overhang on the long sides.
Melt the butter in a 2-quart / 1.9 L saucepan over medium heat, swirling often, until it turns amber and smells nutty, 5 to 7 minutes. Pour into a large mixing bowl and cool for 5 minutes.
Whisk the brown sugar, granulated sugar, and 90 g honey into the warm browned butter until glossy and combined.
Add the eggs and vanilla. Whisk hard for about 1 minute until the mixture lightens in color and thickens slightly.
Add the flour, baking powder, baking soda, and fine sea salt. Fold with a spatula just until no dry streaks remain, don't overmix.
Spread the batter evenly into the prepared pan with an offset spatula, pushing it into the corners.
Bake for 25 to 28 minutes, until the edges are deep golden and a toothpick from the center comes out with a few moist crumbs, not wet batter.
Cool in the pan for 10 minutes. Warm the remaining 60 g honey for 15 seconds and drizzle over the top. Sprinkle with flaky sea salt while it's still warm and sticky.
Cool completely, about 30 minutes, before lifting out with the parchment overhang and slicing into 16 bars.