For the crust, heat oven to 350 degrees. Line a 15-by-10-inch, shallow baking pan (about 1 inch deep) with foil, leaving a 2-inch overhang on the two short sides. Butter the foil on all sides and the bottom.
Blend flour, brown sugar and salt in a food processor, then add butter and pulse until the mixture looks like very coarse cornmeal. Take the mixture and press it down firmly into the prepared pan, pressing on it with the flat side of a metal spatula. Bake until firm to the touch, about 15 minutes; cool in the pan on a rack.
For the topping, in the food processor used to make the crust, pulse the cranberries until coarsely chopped; set aside. Add the hazelnuts and pulse until coarsely chopped; set aside.
Melt the butter in a medium saucepan over moderate heat and stir in sugar, corn syrup and salt. Boil over moderately high heat, stirring occasionally — until the caramel registers 245 degrees on a candy thermometer — for about 8 minutes. Carefully stir in the chopped cranberries, then boil until the caramel returns to 245 degrees, another 6 to 8 minutes.
Remove the pot from the heat and stir in vanilla and the hazelnuts until well coated. Working quickly, use a soft spatula to evenly spread the caramel topping over the crust. Cool completely.
Lift the foil out of the pan. Place it on a cutting board or a clean surface and using a sharp knife, cut the bars in 30 medium pieces or 36 small pieces. Sprinkle lightly with the coarse sea salt.

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