1. Prepare the gnocchi: Place the ricotta in a tea towel and squeeze to force out the excess moisture. Set it aside.
2. Bring a pot of salted water to a boil, and plunge in the pea shoots. Cook until the leaves are tender but still green, 2 to 3 minutes. Drain the leaves in a strainer and run them under cold water to set their color and cool them. Press the leaves between your hands to remove the excess water, and pat dry between paper towels.
3. In a small food processor or blender, combine the leaves with the ricotta and olive oil. Process until smooth. Add the flour, season with salt and white pepper to taste, and pulse just to blend. Then taste, and adjust the salt and pepper if necessary. Press the gnocchi mixture through a sieve into a bowl.
4. Bring 1 quart of water to a boil in a saucepan, and add 1½ heaping teaspoons salt. Then lower the heat to a gentle simmer. Set a bowl filled with ice cubes and water close to the stove. Using two teaspoons, make gnocchi dumplings, about 1 inch in diameter, by picking up some of the gnocchi mixture on one spoon and scraping it off into the simmering water with the other. Poach the gnocchi in three batches, cooking each batch for 4 to 5 minutes. With a slotted spoon, transfer the gnocchi to the ice-water bath.
5. When the gnocchi are cold, use the slotted spoon to transfer them to a plate. Drizzle a little olive oil over them, cover with plastic, and refrigerate until needed. (They can be prepared up to 6 hours in advance.)
6. Prepare the broth: In a medium sauté pan, heat the butter over medium heat. Toss in the scallions, shallot, and rosemary and cook, stirring, until the shallots are translucent but not colored, 3 to 4 minutes. Add the carrots, garlic, and stock, and cook for 3 minutes. Add the morels and salt and white pepper to taste, cover, and cook for another 5 minutes. Uncover the pan, add the peas, and cook for 4 to 5 minutes more.
7. Check the liquid in the pan to make sure it is at a very gentle simmer. Then add the gnocchi, pea shoot leaves, and olive oil. Heat the gnocchi gently for 3 minutes, then add the radishes. Taste the broth, and add more salt and pepper, stock, or olive oil, if needed. Remove the pan from the heat.
8. Lift the gnocchi and vegetables from the pan with a slotted spoon, and divide them among 4 warmed shallow soup plates. Pour an equal amount of broth over each serving, sprinkle with the chives, and serve immediately.