Heat the oven to 350°F. Arrange eight 4-oz. ramekins in a 9 x 13-inch baking pan. Coat the ramekins lightly with cooking spray.
In a small saucepan, heat 1/3 cup of the sugar over medium heat, stirring constantly, until it melts and forms a medium-brown caramel, about 7 minutes. Working quickly, transfer 2 tsp. of the caramel to each ramekins, swirling as soon as you spoon in the caramel (it will harden quickly). Set aside.
Combine the whole milk and evaporated milk in a medium saucepan over medium heat until warm. Reduce the heat to a low simmer and keep warm.
Meanwhile, bring 4 cups water to a boil and keep hot.
Whisk together the whole eggs, egg yolks, the remaining 1/3 cup sugar, the vanilla, cinnamon, and nutmeg in a medium bowl. Fold in the pumpkin, then fold the pumpkin mixture into the warm milk mixture. Divide the filling among the ramekins, then place the baking pan in the oven. Pour the hot water into the baking pan until it reaches halfway up the sides of the ramekins. Bake until the flans are just set, 35 to 40 minutes. Let cool completely.
Place a dessert plate on top of each ramekin and invert; the flan should slide out and syrup should flow onto the sides of the dish.
The flans may be baked, cooled, and plated several hours ahead, covered with plastic wrap, and refrigerated.