For Brownies: Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9 x 13 baking dish.
Combine the melted butter, sugar, and vanilla in a large bowl. Beat in the eggs, one at a time, mixing well after each, until thoroughly blended.
Sift together the flour, cocoa powder, and salt. Gradually stir the dry mixture into the wet mixture until blended. Stir in the chocolate morsels. Spread the batter evenly into the prepared baking dish.
Bake in preheated oven until an inserted toothpick comes out clean, 35 to 40 minutes. Remove, and cool pan on wire rack before cutting.
For Salted Caramel Sauce: In a heavy-bottomed saucepan, combine the sugar and water over medium-low heat until the sugar dissolves. Increase the heat and bring to a boil, without stirring. If necessary, use a wet pastry brush to wash down any crystals on the side of the pan. Boil until the syrup is a deep amber color, about 5 to 6 minutes. Remove the sugar from the heat and carefully whisk in the heavy cream. The mixture will bubble. Stir in the unsalted butter, and salt. Transfer the caramel to a dish and cool.