Set a rack in the middle of the oven and preheat to 350°. Boil 1 quart of water. Arrange the greased ramekins in the baking dish.
CARAMEL: Combine the sugar and water in the small saucepan. Bring to a boil over medium-high heat, stirring with a fork, just until the sugar dissolves, about 3 minutes. Stop stirring to prevent the sugar from crystallizing. Let the sugar continue to cook and gradually caramelize until deep golden brown, about 4 minutes more. Remove from heat and carefully divide the hot caramel between the 8 prepared ramekins to form a layer in the bottom of each. Allow to cool.
CUSTARD: Put 6 tablespoons of the sugar, the milk, vanilla, and bourbon into the 1-quart saucepan. Bring just to a boil over medium-high heat, then remove from the heat. In the small mixing bowl, whisk the remaining sugar with the cinnamon, ginger, allspice, and nutmeg. In the 3-quart mixing bowl, whisk the eggs just until the yolks are broken and mixed with the whites. Add the sugar mixture and whisk until thoroughly combined with the eggs, then whisk in the pumpkin puree until thoroughly combined. Add the hot milk mixture a little at a time, whisking constantly, until well combined. Skim off any foam from the surface.
BAKE: Carefully pour the custard mixture evenly into the ramekins. Pull the oven rack about halfway out of the preheated oven and put the baking dish onto the rack. Pour in hot water from the kettle until it comes halfway up sides of the ramekins. Gently slide the rack back into the oven and close the door. Bake until the flans are set around the edges but still slightly wobbly in the center, about 25 to 30 minutes. Carefully remove the baking dish from the oven and set on a cutting board. Let the flans rest in the water bath for 5 minutes, then remove and transfer to the refrigerator to chill completely, at least 2 hours.
SERVE: Let the flans stand at room temperature for about 10 to 15 minutes. Carefully run a sharp knife around edges of each ramekin. Dip the bottoms of each ramekin briefly into a bowl of hot water to warm the caramel slightly. Invert the flans onto dessert plates, tap the bottoms to release, and carefully lift the molds. The caramel should run down the sides and form a pool on the plate.