In a large saucepan of boiling salted water, cook the cipollini for 5 minutes. Drain well and peel the onions, then transfer them to a clean 1-quart heatproof jar.
Put the fennel seeds, peppercorns, coriander seeds and bay leaf in a tea ball or tie them in a cheesecloth bundle. In a saucepan, cover the ball or spice bundle with the vinegar, water, sugar and 1/4 cup of kosher salt and bring to a boil, stirring to dissolve the sugar and salt. Pour the brine and the spice bundle over the onions and let stand at room temperature for at least 4 hours or refrigerate overnight.
Meanwhile, in a large pot of boiling salted water, cook the carrots until tender, about 10 minutes. Drain and pat dry.
In a large, deep skillet, melt the butter in the oil. Add the scallion greens and cook over moderately high heat until softened and lightly browned, about 1 minute. Add the carrots and peas and cook until heated through, about 3 minutes. Drain and thinly slice half of the pickled onions and add them to the vegetables. Cook until just heated through, season with salt and pepper and serve.