Heat oil in a large heavy pot over medium heat. Add chorizo and cook, stirring often, until some fat has rendered and chorizo begins to crisp, about 4 minutes.
Add potatoes, spring onion whites, and garlic. Cook, tossing often, until potatoes are crisp-tender, 10-12 minutes. Add wine and cook until reduced by half, about 5 minutes. Add 2 1/2 cups water and continue to cook until potatoes are just tender, 5-8 minutes longer.
Add clams and half of onion greens, cover pot, and cook, stirring occasionally, until clams have opened, 8-10 minutes (discard any clams that do not open).
Divide clam mixture among bowls. Top with remaining onion greens and serve with toast.