Set your oven on broil. If you don't have a broil setting, then set your oven for maximum temperature. Place a large pan of water to boil.
Put the peppers onto a baking sheet. Once the oven is at broil temperature put your peppers in the oven. Be sure to leave the oven door open slightly, if you are broiling, so you don't overcook!
Now the water should be boiling. Put your asparagus in the water and set your timer for two minutes.
Check the peppers, once they are burnt (yes, burnt) over most of the topside, then you take them out and turn them to roast on the other side. Repeat this until the whole outside of the pepper is mostly burnt. Remember it doesn't have to completely burnt, just burnt over 75% of a side. If you are baking, you'll turn them only if the topside is not browning well enough, the pan side might burn first due to the metal pan.
When the asparagus is done, put them in a strainer and immediately run them under cold water to cool them and stop the cooking process. Set aside.
When the peppers are done, place them in an ice bath and let cool.
When the peppers are cooled, you peel off the outside, burnt layer and cut them into long strips about an inch wide, making sure to wash off any seeds.
Put the asparagus and pepper strips into a bowl and pour the vinaigrette overtop. Cover and set the dish in the refrigerator to marinate at least 3 hours, 12 hours is preferable.
When you are ready to serve the appetizer, take your dish out and arrange the peppers in a fan pattern. Then arrange the asparagus overtop in a similarly. Put the onions and capers in little piles towards the top of the plate.
Sprinkle liberally with the cheese, as much as is preferred, and garnish with a sprig of basil or mint leaf.