Bring water and granulated sugar to a boil in a 2-quart heavy saucepan over medium heat, stirring until sugar is dissolved. Continue to cook, stirring occasionally, until water has been reduced and mixture forms large bubbles and turns a medium amber color. This should take about 5-6 minutes. If the color is not changing at 5 minutes, increase the heat. Watch the mixture carefully, once it begins to turn color, as it will change quickly.

Carefully add the cream (mixture will bubble up and steam). The caramel will seize up a bit and form some hard shards. Continue to cook and stir until the caramel shards are completely dissolved (2-4 minutes). Add the brown sugar and stir until dissolved.

In the empty bowl (where the cream was) whisk together the egg yolks and vanilla. Add the egg yolks in a SLOW, STEADY stream to the cream mixture, whisking continuously. (Adding the eggs slowly will keep them from scrambling in the hot cream mixture.)

Pour the butterscotch through a fine-mesh sieve back into the egg yolk bowl. Skim off any foam with a spoon. Divide custard among ramekins or pots. Pour hot water around the ramekins to reach about halfway up their sides. Bake, uncovered, until the pots de crème are set around the edges, but still tremble slightly in centers, about 35-40 minutes.

Cool to room temperature in water bath. Pots de crème will continue to set as they cool. If not serving within a few hours, cover and refrigerate. 

Remove from refrigerator 1 hour before serving.

Serve with a sprinkle of flaky sea salt and a dollop of whipped cream.