In a small skillet, melt [1⁄2] tablespoon of butter. Add the sliced onion and saute on medium heat until browned and softened, about 5-6 minutes. Remove the onions and set aside. Melt another [1⁄2] tablespoon of butter in the pan and add the asparagus, mushrooms, and garlic. Season with a pinch of salt and ground pepper, and saute over medium heat until the mushrooms have softened and the asparagus is cooked al dente, about 3-4 minutes. Remove the pan from the heat and set aside.
Spread 1 tablespoon of butter on each slice of bread. Flip over the bread so that the butter side is down. Spread [1⁄2] tablespoon of grainy mustard on each slice of bread.
Remove the bloomy rind from the brie cheese and slice it into 3-4 pieces. Lay the brie on one side of the bread (on top of the mustard), and top that with the sauteed veggies. Add the caramelized onion, and finish with the provolone cheese. Top the sandwich with the second slice of bread (mustard side in) and give it a gentle press to seal all of the ingredients inside.
Place the buttered sandwich in a cold pan and turn the heat to medium-low. Cook on one side until evenly browned and crisp, about 3-4 minutes. Flip the sandwich and cook on the other side for another 3 minutes, until the cheeses are melted and the crust is nicely browned. Slide the grilled cheese out of the pan, cut it crosswise to enjoy the view of bright green asparagus and gooey cheese. Then, just bite in, stretch that cheese, and enjoy!