Brown the butter: Melt 1 cup unsalted butter in a medium saucepan over medium heat. Swirl occasionally as it foams and sizzles. After 5 to 6 minutes, dark golden specks will form at the bottom with a nutty aroma. Immediately pour into a mixing bowl to stop cooking and cool for 15 minutes.

Whisk the cookie dough: Whisk the dark brown sugar and granulated sugar into the warm browned butter until smooth. Add egg, egg yolk, and vanilla extract; whisk vigorously for 1 minute until glossy and emulsified. Stir in the flour, baking soda, cinnamon, and fine salt with a rubber spatula just until combined into a soft dough. Chill dough in the refrigerator for 20 minutes.

Bake and press wells: Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper. Scoop dough using a 2-tablespoon cookie scoop and place 2 inches apart. Bake for 9 to 10 minutes until edges are lightly golden and set. Immediately remove from oven and gently press the back of a rounded tablespoon into each cookie center to create a deep well.

Make gooey pecan pie filling: While cookies bake, melt 3 tablespoons butter, brown sugar, maple syrup, and heavy cream in a small saucepan over medium heat. Simmer gently for 2 minutes until bubbly, thick, and glossy. Stir in chopped toasted pecans and vanilla; remove from heat.

Fill and set: Spoon a heaping tablespoon of warm gooey pecan pie filling into each cookie well. Sprinkle lightly with flaky Maldon sea salt. Allow cookies to cool on the baking sheet for 15 to 20 minutes so the caramel filling sets into a luscious, soft, sliceable center!