In a small bowl, mix together the cheese and tarragon. Butter all the bread slices on one side only. Put four slices, buttered side down, on a cutting board. Distribute the cheese over the bread and top with the ham, folding the slices if they're large. Spread about 1-1/2 teaspoons mustard on the unbuttered side of the remaining bread slices and set them, mustard side down, on top.

Heat a large nonstick pan or griddle over medium-high heat for 2 minutes. Put as many sandwiches as will fit in the pan or on the griddle without crowding, cover, and cook until the cheese has just begun to melt and the bread is golden broown, about 2 minutes. Remove the lid and turn the sandwiches, pressing each one firmly with a spatula to flatten it slightly. Cook the sandwiches uncovered until the bottom is golden brown, about 1 minute. Turn them once more and press with the spatula again to recrisp the bread, about 30 seconds. Cut the sandwiches in half and serve immediately, with more mustard on the side.