In a food processor place the olive oil, the bunch of basil, pine nuts, and garlic. Blend the ingredients together until a paste is formed. Add the salt and white pepper, and stir them in. Set the pesto aside.
In a large skillet place the butter and heat it on medium high until it has melted. Add the shallots, the 1 tablespoon of basil, broccoli, carrots, zucchini, and snow peas. Saute the vegetables for 3 to 4 minutes, or until they are cooked al dente.
Add the heavy cream and stir it in. Bring the ingredients to a boil. Add the cooked pasta and stir it in. Add the pesto to the angel hair pasta and stir it in well. Season the dish with the salt and the white pepper.
On each of 4 individual serving plates place the pasta. Sprinkle the parmesan cheese on top.