In a large saucepan, combine the maple syrup, brown sugar, water and fine sea salt and bring to a boil over medium-high heat. Simmer for about 5 minutes over medium heat, stirring occasionally, until the mixture darkens and thickens. Remove from the heat and whisk in the half-and-half and 1/2 cup of whipped cream until smooth.
In a large bowl, whisk the eggs and cornstarch until smooth. Add to the brown-sugar mixture in a slow, thin stream, whisking steadily. Return the pan to the heat and cook over medium heat, whisking constantly, until it thickens to the texture of pudding, about 5-7 minutes.
Divide the budino among four 8-ounce ramekins or glasses and sprinkle each with fleur de sel. Cover and refrigerate for at least 2 hours or up to overnight.
Whisk the remaining cream in a cold bowl (preferably metal) until thick.
Top the puddings a dollop of whipped cream and some chocolate shavings and serve.