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Step 1
In a 1-quart saucepot over medium-high heat, combine sugar along with 2 tablespoons water and stir with a fork until the sugar dissolves and the mixture begins to simmer, 2 to 3 minutes. Cover and cook until the sugar just starts to caramelize, 3 to 5 minutes. Remove lid and cook until the sugar becomes a deep caramel, swirling the pan as needed for even cooking, about 1 minute. Remove from heat and carefully add the cream followed by the olive oil and stir to combine (the mixture will vigorously foam up, so take care to keep your hands away from the steam). Stir in the salt, pour into a heatproof bowl, and set aside to cool.
Step 2
Caramel can be made up to 3 days in advance and stored covered at room temperature.
Step 3
In a large bowl, whisk together the olive oil, brown sugar, kosher salt, and baking powder. Whisk in the eggs, one at a time, until creamy and combined. Set the mixture aside for 20 to 40 minutes, whisking occasionally (this dissolves some of the sugar and results in a chewier blondie).
Step 4
Meanwhile, lightly grease a 9x9-inch baking pan with olive oil and line the bottom and two sides with a sheet of parchment paper. Set a rack in the lower-middle position in the oven and preheat to 350°F.
Step 5
Add the flour and nuts to the egg mixture and stir to combine. Scrape about two-thirds of the blondie batter into the prepared pan and spread into an even layer with an offset spatula or spoon. Using a teaspoon, dollop the cooled caramel all over the blondie batter followed by dollops of the remaining blondie batter. Using the tip of an offset spatula or butter knife, swirl together the caramel and top layer of blondie batter, taking care not to disturb the bottom layer of blondie batter too much.
Step 6
Lightly sprinkle with flaky salt and bake until the blondie has puffed slightly and the top feels set, about 35 minutes. Cool completely before removing from pan and cutting into pieces. In an airtight container, the cut blondies will keep for a week at room temperature or frozen for 3 months.