Preheat the oven to 350°F (177°C) and line a 9×13-inch metal baking pan with parchment paper, leaving a few inches of overhang on 2 opposite sides.

Make the crust: Place the sliced butter in a light-colored skillet or saucepan over medium heat. Stir or whisk the butter constantly as it melts. After 5–8 minutes, the butter will begin browning. As soon as the butter has browned, immediately remove from heat and pour it into a large heat-safe glass bowl. Allow to cool for about 10 minutes.

Add the sugar, water, vanilla, and salt to the slightly cooled brown butter and stir until combined. Add the flour and cornstarch and mix until the flour disappears. Press the crust evenly into the prepared baking pan.

Bake for 15 minutes or until lightly browned on the edges. Place the baking pan on a cooling rack while you make the topping.

Make the topping: Return the skillet/saucepan to medium heat and add the maple syrup, brown sugar, butter, and cream. Melt the butter, whisking constantly to combine the ingredients. Cool for 5 minutes. Whisk in the beaten eggs, then fold in the pecans. Pour the topping over the warm crust and spread it into an even layer. Lightly sprinkle with sea salt.

Bake for 25 to 28 minutes or until a toothpick inserted in the center comes out mostly clean. If the top is browning too quickly, loosely tent aluminum foil over the pan. Cool the bars completely in the pan set on a cooling rack.

Lift the cooled bars out of the pan by gripping the parchment paper overhang; transfer to a cutting board and use a sharp knife to cut into squares. Store leftover bars covered tightly at room temperature or in the refrigerator for up to 1 week.