Put the clams in a bowl under cold running water. Let the water run over them while you continue.
Trim the green tops from the onion bulbs and thinly slice enough to fill 1/4 cup, and reserve. Peel the bulbs like you would an onion, leaving some of the root. Halve only the largest bulbs, if any. Scrub the clams.
Heat the butter in a large skillet with a lid over medium-high heat until the foam mostly subsides (the butter will start to brown, which is ok). Add the bulbs and cook, stirring, until they start to brown, 2 to 3 minutes. If the butter starts to turn dark brown, reduce the heat a bit.
Stir in 1/4 cup water, the mirin and the miso. Add the clams and turn the heat to medium-high. Cover the pan and cook, shaking the pan occasionally, until the clams open, 6 to 8 minutes. Stir in most of the reserved sliced greens. Ladle the clams and their broth into 4 bowls, discarding any clams that don't open. Garnish with the rest of the greens over the top and serve with cooked rice.
White miso is available at Asian specialty stores and some supermarkets.
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