Brown the butter by melting it in a saucepan over medium-high heat. Once melted, reduce to medium-low and cook until brown bits appear and the butter smells nutty. Remove from heat and let cool slightly.
In a bowl, whisk together flour, baking soda, and salt. Set aside.
Pour the browned butter into a mixing bowl. Add brown sugar and granulated sugar. Mix until combined.
Add the egg and mix until light and fluffy. The mixture should turn a pale caramel color.
Add honey and vanilla extract. Mix until smooth.
Combine dry ingredients with wet ingredients. Mix until just combined. Do not overmix.
Cover and chill the dough for 45 minutes.
Preheat oven to 350°F (177°C). Line baking sheets with parchment paper.
Place sesame seeds in a small bowl. Scoop dough, roll into balls, and coat in sesame seeds.
Arrange cookies 2 inches apart on baking sheets.
Bake for 12–14 minutes until edges are golden brown.
Cool on the baking sheet for 5 minutes before transferring to a wire rack.
These Chewy Honey Sesame Cookies will have crisp edges and soft, chewy centers once fully cooled.