Fill a pot for the pasta with about 6 quarts of water, place over high heat, and bring to a boil.
Peel and finely chop the onion. Put the olive oil in a saucepan or deep 8-inch skillet, add the chopped onion, and place over medium heat. Sauté until the onion turns a rich golden color, about 5 minutes.
While the onion is sautéing, shell the fresh peas, if using.
When the onion is ready, add the peas and season generously with salt and pepper. Stir the peas well, then add about ½ cup water. Cook over
medium heat until the peas are tender, adding water if it evaporates completely before they are done. It should take 15 to 20 minutes for the
peas to become tender. (If using frozen peas, add water only once and cook for 6 to 8 minutes).
When the peas are tender, remove from the heat, take out about half the peas, and puree them. A food mill will make the smoothest puree, but if you dont have one you can use a food processor. Put the pureed peas back in the pan with the whole peas.
Add about 2 tablespoons salt to the boiling pasta water, add the tagliatelle,and stir until all the strands are submerged. Cook until al dente.
After the pasta has cooked for about 2 minutes, add ¾ cup of the pasta water to the pan with the peas and stir well.
When the pasta is done, drain well, toss with the sauce, and serve at once.