Position a rack in the center of the oven and heat the oven to 350°F. Bring a large kettle of water to a boil.
Have ready eight 6-oz. oven-safe ramekins and a heatproof 2-cup measuring cup. Put 1 cup of the sugar in a heavy-duty 3-quart saucepan and stir in 1/3 cup water. Cook over medium-high heat, stirring until the sugar is melted, and bring to a boil, about 2 minutes. Brush the side of the pan with a pastry brush dipped in water to wash away any sugar crystals and continue to cook, without stirring, until the edges of the syrup begin to color, 3 to 5 minutes more. Gently swirl the pan to encourage even caramelization, and cook until the syrup turns dark amber, 1 to 2 minutes more.
Immediately pour the caramel into the measuring cup, then quickly distribute the hot caramel among the ramekins, swirling each ramekin to coat the bottom. Set aside.
Combine the milk and heavy cream in a 3-quart heavy-duty saucepan. If using a vanilla bean, scrape the seeds from the bean into the pan and add the bean. Bring just to a simmer over medium-high heat, about 5 minutes. Remove from the heat.
In a medium bowl, whisk together the egg yolks, whole eggs, the remaining 1/3 cup sugar, and the salt until smooth. Whisk in the sour cream and brandy. Remove the vanilla bean (if used) from the cream mixture and gradually whisk the cream mixture into the egg mixture. If using vanilla extract, stir it in. Skim off any foam.
Stir the custard if using a vanilla bean and pour or ladle it into the ramekins. Set the ramekins in a large roasting pan. Carefully pour the hot water into the roasting pan so that it comes halfway up the sides of the ramekins. Cover loosely with aluminum foil. Bake just until the centers of the custards wobble slightly when jiggled, 35 to 40 minutes.
Carefully transfer the ramekins to a rack to cool to room temperature (silicone-tipped tongs work well for this), about 30 minutes. Chill completely in the refrigerator, at least 4 hours (cover when cold).
About 30 minutes before serving, unmold the custards by placing the bottom of a ramekin in a small bowl of very hot water for 30 seconds to soften the caramel. Run a small knife around the edge of the custard to loosen. Put a small serving plate over the ramekin and invert. Holding the plate and ramekin together, shake firmly up and down, if necessary, to release the custard. Remove the ramekin (some caramel will stay in the ramekin). Repeat with the rest of the ramekins and let the custards stand at room temperature until ready to serve.
The custards can be baked up to 2 days ahead; refrigerate and cover once cold. Unmold them about 30 minutes before serving and let come to room temperature.