Preheat the oven to 350°F (175°C). Lightly butter six custard cups or ramekins and arrange them in a large baking dish.
In a medium mixing bowl, whisk together the eggs, egg yolks, and flour until smooth and uniform.
Add the pumpkin puree, half-and-half, milk, sugar, salt, vanilla extract, cinnamon, nutmeg, and ginger. Whisk until the mixture is thoroughly blended and free of lumps.
Evenly distribute the custard mixture among the prepared cups.
Pour hot water into the baking dish around the ramekins until the water reaches halfway up the sides of the cups. This will ensure even cooking and a delicate texture.
Transfer the baking dish to the oven and bake for approximately 40 minutes, or until the custards are just set in the center. The surface should appear firm, while the interior retains a slight jiggle.
Remove the ramekins from the water bath and allow them to cool to room temperature. Serve either at room temperature or chilled, topped with whipped cream if desired.
