Preheat oven to 375°F with racks in upper and lower third positions. In a small bowl, whisk together flour, salt, and baking soda.
Melt butter in a small saucepan over medium heat. Cook, swirling pan occasionally, until butter browns and smells nutty, 6 to 8 minutes. Transfer to a large heatproof bowl; add sugars and whisk until well combined. Add eggs and vanilla; whisk until smooth. Fold in flour mixture and cornflakes until just combined.
Scoop rounded tablespoons of dough onto parchment-lined baking sheets, spacing 2-inches apart. Sprinkle top of each cookie with a pinch of flaky salt. Bake, rotating pans and rack positions halfway through, until lightly browned around edges, 8 to 10 minutes. Let cool completely on pans.