Step 1

In a large nonstick skillet, cook the sliced sausages over moderate heat, turning once, until browned, about 8 minutes. Transfer the sausages to a plate and wipe out the pan.

Step 2

In a bowl, stir the butter with the shredded cheddar cheese just until combined. Spread the cheddar-butter on one side of each slice of bread; arrange them buttered side down on a work surface. Spread the mustard on the bread and sprinkle the Monterey Jack over the mustard. Top 4 slices with the sausages, halved cornichons and the sliced cheddar. Close the sandwiches, pressing lightly and tucking in any stray cheese.

Step 3

Place the sandwiches in the skillet, cover and cook over moderately low heat until golden on the bottom, 3 minutes. Press with a spatula to flatten slightly, then flip the sandwiches, cover and cook until browned on the bottom, 3 minutes longer; lower the heat if the bread is browned before the cheese melts completely. Transfer the sandwiches to a cutting board and let rest for 2 minutes, then cut them in half and serve with cornichons.