Step 1Heat the oven to 325 degrees. Bring a medium pot of water to a boil.
Step 2In a medium heavy-bottom pan, combine 1 cup plus 2 tablespoons sugar and the corn syrup with just enough water to give the sugar a "wet sand" consistency. Place the pan over medium heat and cook, stirring occasionally, until the sugar comes to a boil (reduce the heat as needed so the sugar does not boil over). Continue to cook until the sugar caramelizes, turning a reddish amber color.
Step 3While the sugar is caramelizing, in a small, heavy-bottom pot, combine the half-and-half, cream and vanilla and heat over medium heat, bringing to a bare simmer. Reduce the heat to low to keep the cream warm as the sugar cooks.
Step 4As soon as the sugar caramelizes, remove from heat and gently pour into the cream mixture (be very careful, as the sugar will steam), stirring to combine. Remove the combined caramel and cream from heat and pour the mixture into a medium bowl set over a bowl of ice water (an ice bath), stirring until it comes to room temperature. Remove from the ice bath and set aside.
Step 5In a separate medium bowl, whisk together the egg yolks with the remaining 2 tablespoons and 2 teaspoons sugar and the salt. Whisk the yolks into the cream mixture, then strain the entire mixture through a fine mesh sieve to remove any lumps.
Step 6Divide the mixture between 8 (6-ounce) ramekins, leaving half-inch space at the top. Place the ramekins in a baking dish, and slide the baking dish onto the center rack of the oven. Add enough boiling water to the baking dish to come halfway up the ramekins.
Step 7Loosely cover the baking dish with foil and bake 20 minutes. Check the custard by gently shaking the dish; if it jiggles gently (as with barely set gelatin), it is set. Otherwise, continue to bake, checking every 5 minutes until the custards are set, up to 30 to 40 minutes total.
Step 8When the custards are set, gently remove the baking dish from the oven, uncover the custards, and cool them (still in the baking dish) to room temperature. Remove the cooled custards from the baking dish and refrigerate until well-chilled, at least 2 hours.
Step 9Before serving, remove the chilled custards and sprinkle a scant teaspoon sugar over the surface of each, spreading the sugar with the back of a spoon to evenly cover the top of each custard.
Step 10Place the ramekins on a baking sheet and place under the broiler just until the sugar melts and caramelizes, 1 to 2 minutes. Alternatively, use a small torch to caramelize the tops of each of the custards.
Step 11Cool the custards for 5 minutes before serving.