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.

Place the sliced butter in a light-colored skillet or saucepan over medium heat. (Light-colored helps you determine when the butter begins browning.) Stir or whisk the butter constantly as it melts. Once melted, the butter will begin to foam. Keep stirring. After 5–8 minutes, the butter will begin browning—you’ll notice lightly browned specks begin to form at the bottom of the pan and it will have a nutty aroma. As soon as the butter has browned, immediately remove from heat and pour it into a large heat-safe glass bowl. Scrape up the browned solids at the bottom of the skillet and add them as well. Allow to cool for about 10 minutes. Do not rinse out the pan.

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. The mixture should be slick. 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.

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. When the butter has melted, remove the pan from heat and pour the mixture into a large heat-safe bowl. 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.