Caramel Pecan Cakes

Bring sugar and 1/2 cup water to a boil in a 12-inch heavy skillet over medium heat, stirring until sugar has dissolved, then wash down any sugar crystals on side of skillet with a pastry brush dipped in cold water. Boil, without stirring, swirling skillet occasionally so caramel colors evenly, until dark amber. Remove from heat and carefully stir in remaining cup water (mixture will steam vigorously and may stiffen). Return to a boil and stir until caramel has completely dissolved. If necessary, simmer until just syrupy, 1 to 3 minutes. Cool to room temperature.
Preheat oven to 350°F with rack in middle.
Toast pecans in a 4-sided sheet pan in oven until fragrant and a shade darker, 8 to 10 minutes. Cool and coarsely chop.
Put 2/3 cup cooled caramel syrup in a bowl (save remainder to use as sauce) and add butter, egg, and cream, whisking well after each addition.
Sift together flour, baking soda, salt, and sugars into a large bowl. Make a well in center, then add caramel mixture and gradually whisk in dry ingredients until smooth. Fold in pecans. Chill, covered, until cold (or 12 to 24 hours for best results).
Preheat oven to 325°F with rack in middle.
Butter and lightly flour ramekins, then cut out and fit a round of parchment paper in bottom of each. Arrange in a 4-sided sheet pan.
Divide batter among ramekins (about 1/4 cup each; batter will be stiff). Bake until cakes just spring back when lightly pressed, 30 to 35 minutes. Cool cakes to warm. Reheat remaining caramel. Invert cakes onto plates, then peel off parchment and spoon some of caramel on top.