Bring a saucepan of lightly salted water to a boil and set up a bowl of ice water. Add the peas to the saucepan and cook until tender, 1 to 2 minutes.
Drain the peas and immediately plunge them into the ice water. Drain the peas again. Reserve 1½ cups of the peas. Puree the remaining ½ cup of peas in a blender with about 1/3 cup or slightly more cold water until very smooth. Set the pea puree and the whole peas aside.
Put the chicken stock in a saucepan and bring it to a simmer.
Melt 3 tablespoons of the butter over medium-high heat in a large sauté pan. Add the shallot and sauté for a few minutes, until translucent. Add the garlic and sauté for another minute, until aromatic. Add the rice and stir until the grains of rice are coated with butter.
Add the wine and simmer, stirring, until most of the wine is absorbed.
Start adding the simmering chicken stock, about 1 cup at a time, adding more chicken stock only once the rice has absorbed almost all of the stock already in the pan. Keep stirring the risotto frequently. Continue adding the stock in smaller amounts as the rice comes closer to being cooked. You may not need all the stock.
After 20 to 25 minutes of this process, the rice should be cooked to the al dente stage. Taste a piece of rice to see if the grain is tender and edible with just a little bit of a bite in the center.
When the rice is al dente, remove the risotto from the heat and stir in the remaining 3 tablespoons butter and the Parmesan.
Add a little more of the simmering stock, about ¼ to ½ cup, to loosen the risotto and make it soupy and creamy in consistency. Add the fresh herbs, the reserved whole peas, and season to taste with salt and pepper.
Ladle the risotto into 6 large shallow soup bowls or onto a large platter. Use a spoon to drizzle the pea puree decoratively over the risotto. Pass more grated Parmesan at the table.