In a food processor, finely chop 2 cups cornichons until they are a coarse paste.
Spread one side of each piece of bread with Dijon. Top each piece of bread with a slice of Gruyere. Place the ham on half of the pieces of the bread and cheese. Spread the cornichon paste on the other half of the pieces of bread and cheese.
Preheat a griddle or saute pan.
Close the sandwiches and press to secure. Butter the outsides of all the pieces of bread.
Place the sandwiches on the griddle or pan and cook until the bread is golden brown, 3 to 4 minutes. Turnover and repeat this process.
When the sammies are golden brown and crisp on each side, remove them from the griddle and neatly cut the crusts off the bread. Cut each crustless sandwich into 8 neat mini sammies.
Top each mini sammie with a cornichon half and secure it with a toothpick.