Put your 3 cups of water in a stock pot, and set that on the stove to boil. When it reaches the boil, pour in your cup of orzo, stir, and reduce the heat to low to medium-low, stirring occasionally. It should only take about 9 minutes for the orzo to be done al dente. When it's done, strain through a strainer, rinse with cold water, and place into a decent sized bowl. Add in your toasted pine nuts, and pour about one tablespoon of olive oil over it, and mix it all together (this will keep it all from sticking togehter). Set this aside.
Next - chop your yellow pepper into roughly bite-sized pieces, and set them aside. Take your asparagus stalks and cut off the bottom inch or so off (as that's far too tough and woody), cut the remaining into quarters (resulting in nice, bite-sized pieces), and set aside. Now take 5 of your basil leaves and loosely chop them up.
Put 2 tablespoons of olive oil into a sauté pan, and set over medium-high heat. Add your yellow pepper, asparagus, basil, salt, and pepper to the pan, and sauté for approximately 5 minutes. After five minutes, add your dry vermouth the pan and quickly flame it off. Kill the heat, and pour the contents of the pan into the bowl that has your orzo and pine nuts in it.
Take your tomato and chop it up, and add this to the bowl, and then take your remaining 8 leaves of basil and slice them nice and thin, and add these to the bowl as well. Mix all of this together with a wooden spoon or a spatula, and set it in the fridge for an hour or so, until it's good and cool.
To serve, either pour it all onto a nice serving dish and garnish with a few sprigs of basil, or portion out into shallow bowls (again, garnishing with a spring of basil).