Bring a pot of salty water to the boil and cook the peas and asparagus for about 2 - 3 minutes. Scoop out with a small sieve and place in a bowl and run under cold water to stop the cooking process (depending on your size of your asparagus, you may need to start coking them before the peas and maybe a bit longer too, just check as you go).
Using the same salty water that you blanched the peas and asparagus in, cook the pasta for 2 minutes less than the instructions say.
Place the oil in a large pan on a medium heat. Add the lemon zest, lemon juice and bring to a simmer. Add the cream and tarragon and season with some salt and pepper (if your pasta has not finished cooking turn the heat down, until the pasta is ready). Once the pasta is cooked, place it straight into the pan and finish the cooking process. It should take about 4 minutes to finish cooking, Half way through add your peas and asparagus so they can warm through. Add the parmesan cheese in 2 batches to the pasta along with the basil and chives. You will have to toss the pasta a bit to make sure it all cooks evenly. Check your seasoning as you go too.
Serve with a good crack of freshly ground black pepper and some parmesan cheese sprinkled on top.