Proceed as for Baked Custard, omitting the sugar. Heat the half-and-half gently but do not combine yet with the eggs and salt.
To prepare the caramel, heat ¾ cup sugar, ¼ cup water, and ¼ teaspoon lemon juice or vinegar in a deep heavy saucepan (use one that seems larger than necessary, as the caramel will bubble up quite a bit) over medium heat, stirring until the sugar is dissolved. Increase the heat to high and bring the syrup to a rolling boil; cover the pan and boil for 2 minutes. Uncover the pan and cook until the caramel begins to darken. When the caramel turns deep amber, remove from the heat and add a little of the half-and-half, stirring. Be careful—the caramel will bubble furiously. Continue adding the half-and-half a little at a time until completely incorporated. If the caramel seizes up, return to low heat and stir until dissolved.
Let the caramel mixture cool for 10 minutes, then whisk into the eggs as directed above and add the vanilla. Strain the custard through a fine-mesh sieve. Proceed as directed, baking the custards for 25 to 30 minutes. When ready to serve, sprinkle the tops of the custards with (flaky sea salt), if desired.