Preheat oven to 350 degrees F. Place the custard cups on a large roasting pan.
Mix the sugar and water into a pot and bring to a boil. Let mixture cook, without stirring, until it turns a light caramel color, about 5 minutes.
Stir in the pecans to coat well and let cook another 3 minutes or until the mixture becomes a dark caramel color. Quickly pour the pecan mixture onto a large nonstick baking sheet and let cool completely. Once it has cooled break into small pieces and evenly sprinkle into the custard cups.
In a pot, mix the milk, cinnamon, cardamom, and cloves; bring to a boil. Cook, stirring often, for 2 minutes.
In the meantime whisk together the brown sugar, eggs, and egg white in a large bowl. When milk mixture is ready whisk into the egg mixture. Stir in the pumpkin and vanilla then evenly divide mixture among the custard cups.
Place hot water into roasting pan until it comes halfway up the sides of the custard cups then place entire pan with cups into the oven and bake until a knife inserted into the center of the custard comes out clean, about 30 minutes. Remove cups from pan, let cool, cover, and refrigerate at least 4 hours before serving.