Preheat oven to 325˚F with a rack in the middle position. Place six 4-6-ounce ramekins in a 2-inch sided baking pan (I use a 9x13-inch cake pan).
Whisk together cream, pumpkin, dark brown sugar and pumpkin pie spice in a medium size bowl (preferably, with a pouring spout). Set aside.
Bring water, corn syrup, maple syrup and the 6 tablespoons granulated sugar to a boil in a 2-quart heavy saucepan over medium heat, stirring with a fork in the center of the pan until sugar is dissolved. Boil without stirring, swirling pan occasionally, until mixture has gone from light to dark amber, about 6-8 minutes. Watch the mixture carefully towards the end as once it begins to turn color it will change fairly quickly.
Remove from heat. Carefully add cream/pumpkin mixture (mixture may bubble up and steam). Whisk until combined. If caramel mixture does not completely dissolve, return pot to heat and stir for a minute or two until dissolved.
Combine the egg yolks and vanilla and whisk until smooth. Add the egg yolks to the hot cream mixture in a SLOW, STEADY stream, whisking continuously. (Adding the eggs slowly will keep them from scrambling in the hot cream mixture.)
Pour custard through a fine-mesh sieve back into the egg yolk bowl. Divide custard among ramekins or pots in the pan. Pour hot water into pan the ramekins are in to reach about half way up the sides. Bake, uncovered, until custards are set around edges, but still tremble slightly in centers, about 35-45 minutes.
Remove from the water bath with a tongs or pot holder. Allow to cool for 20 minutes, then refrigerate until 30 minutes before serving. Remove from refrigerator 30 minutes before serving. Serve with a dollop of whipped cream.