In a large saucepan, cover the eggs with cold water; turn the heat to high and bring to a boil. Boil for 1 minute, then remove from the heat and cover and let stand for 10 minutes.
Remove the eggs from the water and cool under running water, shaking the pan vigorously to crack the shells. Add ice cubes to the pan and cool. Drain and peel the eggs.
Halve the eggs lengthwise, remove the yolks, and reserve. In a food processor, mix the egg yolks, crème fraîche, mayonnaise, and mustard until smooth. Transfer to a bowl and stir in the cornichons, red onions, and green jalapeño sauce, and then season with salt and pepper. Mix in the melted butter until the mixture is fully combine and consistent. Refrigerate the filling until the butter sets, 1 hour.
Arrange the egg whites on a serving platter. Using a pastry bag fitted with a star tip, fill the egg white halves with the yolk mixture.
Garnish with fresh herbs, trout roe, fried oysters, or smoked salmon.