In a small saucepan, bring the cream to a boil. Off the heat, stir in 4 ounces of the chocolate and let stand for 1 minute, then whisk until smooth. Transfer to a bowl and let the ganache cool.
In a food processor, combine the pecans with the flour and salt and pulse until finely ground. In a medium saucepan, combine the butter, brown sugar and corn syrup and bring to a boil, stirring. Remove from the heat and add the vanilla and ground pecan mixture. Transfer the batter to a bowl and refrigerate until firm, about 2 hours.
Preheat the oven to 350°. Scoop 48 level teaspoons of the batter and roll each into a ball. Place 8 balls on a large ungreased cookie sheet, 4 inches apart. Keep the rest of the balls refrigerated. Bake the cookies for 9 minutes, or until they stop bubbling. Set the baking sheet on a wire rack and let the cookies cool for 3 minutes. Working very quickly, form 4 of the cookies into cones: Carefully lift 1 cookie at a time with a spatula and roll it, bumpy side out, into a cone shape. Press the seam to close, transfer to a wire rack and let cool. Transfer the remaining 4 flat cookies to the rack. Repeat with the remaining balls, forming half into cones and transferring the remaining flat cookies to a wire rack to cool. Between batches, run the underside of the baking sheet under cool water and wipe it dry.
Line 2 baking sheets with wax paper. In a small saucepan, melt the remaining 5 ounces of chocolate. Using a small pastry brush, brush the chocolate all over the bumpy surface of the cones and the flat cookies and transfer them to the prepared sheets; warm the chocolate if it becomes too thick. Refrigerate the cookies just until the chocolate is set.
Fill a pastry bag fitted with a 1/8-inch plain tip with the chocolate ganache. Pipe a ring of ganache on a flat cookie, about the size of the rim of a cone. Carefully place the cone on the ganache, holding it in place just until set. Repeat to make the remaining hats. Refrigerate just until chilled. Run a thin knife under the cookies to release them from the wax paper, transfer to a platter and serve.
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