In a medium saucepan, combine the granulated sugar and corn syrup with ¼ cup of water, gently stirring to avoid splashing the sides of the pan. Place the saucepan over high heat and cook the mixture until it reaches 350°F (175°C) on an instant-read thermometer, or until it turns a deep amber color—this typically takes 6 to 8 minutes. Keep a close watch, as caramel can quickly burn once it begins to darken. Once it reaches the desired color, remove the pan from the heat and carefully pour in the heavy cream (it will bubble vigorously). Stir in the fleur de sel, then whisk in the sour cream until smooth. Set the caramel aside to cool.

Preheat your oven to 350°F (175°C). Butter the sides and bottom of a 9×13-inch glass or light-colored metal baking pan. Line the bottom with parchment paper and lightly butter the parchment as well. In a medium mixing bowl, whisk together the flour, salt, and Dutch-process cocoa powder.

In the bowl of a double boiler set over gently simmering water, add the chopped chocolate and butter. Stir occasionally until the mixture is completely melted and smooth. Turn off the heat, but leave the bowl over the warm water and whisk in the granulated sugar and brown sugar until fully incorporated. Remove the bowl from the double boiler—the mixture should be close to room temperature at this point.

Add three of the eggs to the chocolate mixture and whisk just until blended. Then add the remaining two eggs and whisk again, being careful not to overmix. Stir in the vanilla extract until combined. Avoid overbeating the batter here, as that can result in a cakier texture instead of the desired fudgy consistency.

Sprinkle the dry ingredients over the chocolate mixture. Using a spatula, gently fold the flour mixture into the wet ingredients, stopping when only a few streaks of flour remain visible—don’t overmix.

Pour half of the brownie batter into the prepared pan and smooth the surface with a spatula. Drizzle approximately ¾ cup of the cooled caramel sauce over the brownie layer in a zigzag pattern, taking care to avoid the edges of the pan (caramel near the edges tends to burn). Use an offset spatula to gently spread the caramel over the brownie base, leaving a ½-inch border around the perimeter. Spoon the remaining brownie batter in generous dollops over the caramel layer and carefully smooth the top to completely cover the caramel without disturbing the layers.

Place the pan in the preheated oven and bake for 30 minutes, rotating the pan halfway through to ensure even baking. Check for doneness by inserting a toothpick into the center—it's ready when it comes out with just a few moist crumbs attached.

Once baked, remove the brownies from the oven and immediately sprinkle the top with the fleur de sel and coarse sugar. Allow the brownies to cool completely in the pan before cutting. For clean slices, use a sharp knife and wipe it between cuts. These brownies can be stored in an airtight container at room temperature for up to 4 days, and they also freeze exceptionally well for longer storage.