Step 1

Melt 1/2 cup butter in a medium skillet over medium heat. Cook, swirling the pan, until the butter tums golden brown, 3 to 4 minutes. Pour the browned butter into a large heatproof bowl. Swirl the bowl gently to stop the cooking, then let cool completely, about 45 minutes. Meanwhile, leave the remaining 1/2 cup butter at room temperature to soften.

Step 2

Position racks in the upper and lower thirds of the oven and preheat to 375°F. Line 2 baking sheets with parchment paper. Add the softened butter, brown sugar and granulated sugar to the bowl with the cooled browned butter and beat with a mixer on medium-high speed until combined, about 2 minutes. Add the eggs and vanilla and beat until smooth, scraping down the sides and bottom of the bowl as needed, about 1 minute.

Step 3

In a medium bowl, whisk together the flour, baking soda and salt. Add to the butter mixture and beat on low speed until just combined. Scrape down the bowl and beat for a few more seconds.

Step 4

Scoop and roll the dough into 1¼-inch balls. Arrange about 2 inches apart on the prepared baking sheets. Bake, switching the pans halfway through, until the cookies are golden, 9 to 12 minutes. Let cool for 2 minutes on the baking sheets, then transfer to a rack to cool completely. Store in an air-tight container for up to 3 days.

Step 5

Just before serving, drizzle the cookies with caramel sauce and sprinkle with flaky sea salt.