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MAKE CARAMEL:
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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.
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Boil, without stirring, swirling skillet occasionally so caramel colors evenly, until dark amber.
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Remove from heat and carefully stir in remaining cup water (mixture will steam vigorously and may stiffen).
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Return to a boil and stir until caramel has completely dissolved.
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If necessary, simmer until just syrupy, 1 to 3 minutes.
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Cool to room temperature.
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TOAST PECANS FOR CAKE:
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Preheat oven to 350°F with rack in middle.
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Toast pecans in a 4-sided sheet pan in oven until fragrant and a shade darker, 8 to 10 minutes. Cool and coarsely chop.
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MAKE CAKE:
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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.
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Sift together flour, baking soda, salt, and sugars into a large bowl.
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Make a well in center, then add caramel mixture and gradually whisk in dry ingredients until smooth.
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Fold in pecans.
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Chill, covered, until cold (or 12 to 24 hours for best results).
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Preheat oven to 325°F with rack in middle.
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Butter and lightly flour 8 (6-ounces) ramekins, then cut out and fit a round of parchment paper in bottom of each.
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Arrange in a 4-sided sheet pan.
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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.
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Reheat remaining caramel. Invert cakes onto plates, then peel off parchment and spoon some of caramel on top.
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NOTE:
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Cakes can be made 4 hours ahead. Rewarm, individually wrapped in foil, in a 300°F oven.