Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone mat.
Brown the butter: melt it over medium heat and simmer until it smells nutty and turns a light amber. Remove from heat and let cool slightly.
In a mixing bowl, whisk together the browned butter, granulated sugar, and brown sugar until smooth.
Add the eggs and vanilla. Mix until the mixture is glossy and combined.
In another bowl, whisk the flour, salt, and baking soda. Gradually fold the dry ingredients into the wet mixture until just combined.
Drop tiny spoonfuls (about 1 teaspoon each) onto the prepared sheet, leaving plenty of space.
Baking
Bake for 8–10 minutes, watching closely. Edges should be golden and centers set.
Let the cookies cool on the pan for a few minutes, then transfer to a rack.
Assembly
When completely cool, pair cookies into sandwiches with a small dollop of Nutella between two cookies.
Finish each with a tiny pinch of sea salt.
Notes
Browned butter is optional but highly recommended for a toasted, caramel note. For a dairy-free swap, use vegan butter. Avoid freezing assembled sandwiches to prevent sogginess.