Begin by making the mazetta: Using an electric mixer, beat egg whites until stiff; set aside. In a 1-quart saucepan, combine corn syrup, 1/4 cup water, and sugar. Clip on a candy thermometer. Bring to a boil over high heat, stirring with a wooden spoon, about 5 minutes. Wash down sides of pan with a pastry brush dipped in water to remove any sugar crystals.
Cook over medium heat, stirring occasionally, until temperature reaches 242 degrees (soft-ball stage), 15 to 20 minutes. Remove sugar syrup from heat. Beating constantly on medium speed, slowly pour hot syrup into egg whites. Continue beating for 3 to 4 minutes until syrup is incorporated. Use immediately or cover and refrigerate until ready to make the nougat.
Spray an 8-inch square baking pan with vegetable-oil spray; set aside. Place mazetta in a large bowl; set aside. In a 2-quart saucepan, combine corn syrup and sugar. Clip on candy thermometer. Bring to a boil over high heat, stirring constantly with a wooden spoon, 5 to 10 minutes. Wash down sides of pan with a pastry brush dipped in water to remove any sugar crystals.
Over medium-high heat, cook to 280 degrees (soft-crack stage), 12 to 15 minutes, without stirring. If heat is too high it can boil over, so watch carefully. Remove from heat; let stand for 2 minutes. Without scraping pan, pour syrup over mazetta. Working quickly, stir with a wooden spoon until almost smooth. Stir in butter, vanilla, and salt. Mix until butter is incorporated. Stir in nuts. Scrape into prepared pan, and smooth the top; you may spray your hand with vegetable-oil spray and run it over the warm candy to smooth it. Let stand at room temperature, uncovered, until firm, 4 to 6 hours.
Spray a large cutting board generously with vegetable-oil spray. Unmold nougat from pan onto sprayed surface. Cut nougat into 3-by-1-by-3/4-inch pieces or other desired shapes. Wrap each piece in cellophane or waxed paper.