Step 1Shuck the beans into a work bowl. Cover the beans with boiling water and set aside until cool enough to handle. Cut a nick in the bottom of the skin of each bean with your thumbnail and squeeze the inside beans from the skin. You should have 2 1/2 to 3 cups fava beans.
Step 2In a large skillet, heat one-fourth cup olive oil over medium heat and add the green onion and lemon zest. Add the fava beans, the white wine and 1 teaspoon salt, and simmer until the beans are just tender, about 7 to 10 minutes. Remove from the heat, stir in the mint and cool until ready to serve.
Step 3When ready to serve, mound the favas on a plate. Cut each burrata ball into quarters and arrange them over the top. Season the burrata with a little more salt and freshly ground pepper, and drizzle lightly with olive oil. Scatter the chopped pistachios over the top and serve.