Preheat oven to 350°F (175°C).
In a medium saucepan, mix sugar and water over medium heat. Stir just until dissolved, then cook without stirring until it turns a deep golden caramel, about 5–7 minutes.
Carefully pour the caramel into a flan mold or 9-inch round baking dish, swirling to coat the bottom evenly. Set aside to cool and harden.
In a blender, combine evaporated milk, condensed milk, whole eggs, egg yolks, pumpkin purée, pumpkin pie spice, vanilla, and salt. Blend until completely smooth and silky. For the smoothest texture, strain through a fine-mesh sieve directly into the caramel-lined mold.
Place the mold inside a larger baking dish and pour in hot water until it reaches halfway up the sides. Cover tightly with foil and bake for 60–65 minutes, until the center is just set but still has a slight jiggle.
Remove from the water bath and let cool to room temperature. Cover and refrigerate for at least 4 hours or overnight for best results.
When ready to serve, run a spatula around the edges, place a serving plate on top, flip carefully, and lift the mold.
The caramel will flow beautifully over the top.
Slice, serve chilled, and enjoy.