Slice sausages in half lengthwise and then cut into thin halfmoon shapes.
Cook sausage in a large nonstick skillet over medium heat, stirring occasionally, until nicely browned, about 6-8 minutes. Remove sausage from pan with a slotted spoon and place in a bowl. Wipe skillet clean to use for grilling the sandwiches.
In a medium bowl, stir together cheddar cheese and 3 tablespoons butter until well mixed.
Spread remaining 2 tablespoons butter on 1 side of each piece of bread.
On four slices of bread, spread the cheddar/butter mixture on the non-buttered side. Top the cheddar with the Andouille sausage. Sprinkle the Monterey Jack cheese on top of the sausage.
Taking the remaining 4 pieces of bread, spread the Dijon on the non-buttered side and place on top of the slices layered with filling, placing the Dijon side down.
Heat skillet over medium heat and add 2 sandwiches at a time. Cook until nicely browned on bottom. Press with spatula to flatten some and flip to other side. Cook until second side is nicely browned. If cheese still isn't completely melted, turn heat to low and cook until cheese melts.
Repeat with remaining 2 sandwiches.