Heat a large skillet over medium heat and cook the bacon until nice and crisp. Remove to a paper towel lined plate until ready to use.
Drain the bacon greats and wipe the skillet out with a paper towel, the remove to the stove. Heat over medium-low heat and add the olive oil. Add the asparagus and garlic, and sprinkle with salt and pepper. Cook, stirring often, until the asparagus has softened and looks a bit roasted. Remove it and set it on a plate.
To prepare the grilled cheeses, spread the insides of the bread with the Dijon mustard. The top two of the bread slices with half of the cheese, half of the bacon slices, half the asparagus, and then the other half of the cheese and top pieces of bread. (If you make three sandwiches using smaller bread, split the ingredients into thirds, versus halves.)
Wipe out your skillet again and return to the stove, over medium heat. Add half of the butter and allow to melt. The carefully place your prepared sandwiches into the skillet and allow to cook for a couple of minutes, until nicely browned and crisp. Carefully flip and repeat until browned and the cheese is good and melted.
Remove from the skillet, allow to sit for just a minute, then slice each sandwich in half, and serve!