Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper and spread half of the toasted sesame seeds evenly across it, creating a sticky layer.
In a mixing bowl, combine the melted butter, honey, vanilla extract, and salt. Whisk together until well blended and glossy.
Add the sifted flour to the wet mixture and stir until a smooth, thick dough forms.
Divide the dough into 12 equal portions. Roll each into a thin disk about 3-4 inches in diameter. Place each disk onto the sesame-coated baking sheet, pressing gently to flatten and ensure good adhesion of sesame seeds.
Brush the tops of each cookie with the beaten egg and sprinkle the remaining sesame seeds on top, pressing lightly to embed them. Bake in the preheated oven for about 12-15 minutes, or until the edges are golden brown and the sesame seeds are toasted.
Remove from oven and let the cookies cool on a wire rack. Once cooled, brush each with warmed honey for a glossy finish and additional flavor.
