Preheat oven to 350 degrees. Spray or butter an 8-inch square baking pan; line pan with parchment paper, pressing against sides (leave overhang intact for easy removal of brownies). Butter or spray parchment paper. Whisk sugars and vanilla with butter until combined. Add eggs, one at a time, whisking until light and well incorporated. Sift together flour, cocoa and salt. All at once, add dry ingredients to wet mixture, scraping down sides of bowl and stirring gently with spoon or spatula until no dry spots remain; do not overmix. Stir in 3/4 c chocolate chips, reserving the rest for topping.
Spoon half of the brownie mixture into prepared pan, spreading into a thin layer across entire pan. Drizzle, but do not spread, caramel sauce over brownie mixture in pan, allowing for some pooling so pockets of caramel will develop when baking. Spoon remaining brownie mix over the caramel, gently spreading; brownies will look rough, with some caramel exposed. Sprinkle with flake salt and scatter remaining chocolate chips over the top.
Bake 30 min, until center is set (it should not wiggle when pan is bumped lightly). Cool completely; when cool, lift brownies from pan using parchment overhang. Peel paper away and cut into squares. Serve at room temperature, with a scoop of vanilla ice cream, if desired. Store any extras chilled in an airtight container.