In a large bowl, toss the shredded cabbage with 1 teaspoon of the salt and let stand for 15 minutes. Drain the cabbage and return it to the bowl.
In a blender, combine the mayonnaise, ketchup, cornichons, shallot, Worcestershire sauce, chili-garlic paste and the remaining 1/2 teaspoon of salt and puree. Season the dressing with pepper and pour it over the drained cabbage; toss well.
Preheat a griddle over moderately high heat. Butter the bread slices and place 4 of them on the hot griddle, buttered side down. Top each one with a slice of cheese, then top 2 of the slices with half of the sliced turkey. Grill until the cheese is melted and the bread is toasted, 2 to 3 minutes. Remove from the griddle. Spoon a generous scoop of the spicy slaw on top of the turkey and close the sandwiches. Repeat to make the remaining 2 sandwiches. Cut the sandwiches in half and serve.