Make the salted caramel: In a heavy-bottomed saucepan, bring the sugar, corn syrup and water to a boil over high heat, swirling (not stirring) to caramelize evenly. When the caramel reaches a dark amber color (about 3 minutes), remove from the heat and carefully add the cream. (The mixture will foam up.) Add the butter, sea salt and vanilla and whisk to combine. Set aside and reserve.
Make the pudding: In a saucepan, combine the maple syrup, brown sugar, water and salt and bring to a boil over medium-high heat, stirring occasionally. Simmer for about 5 minutes, until the mixture darkens slightly in color. Remove from the heat and whisk in the half-and-half until smooth.
In a large, heatproof mixing bowl, whisk the whole egg with the egg yolks and cornstarch until combined. Whisk in the maple-syrup-brown-sugar mixture in a slow, thin stream. Pour the mixture into the saucepan through a fine-mesh strainer and cook over medium heat, whisking constantly, until it thickens to a puddinglike texture, about 5 minutes.
Divide the pudding among four 8-ounce ramekins or small mason jars and top each with a quarter of the reserved caramel. Cover and refrigerate for at least 2 hours or up to overnight. Sprinkle the top of the puddings with sea salt and a dollop of whipped cream before serving.