Shuck oysters and reserve liquor. Place a heavy pan over medium heat and add olive oil and butter. When it shimmers, add shallots and cook gently until soft. Add garlic and continue to cook for 5 minutes, until garlic is soft as well. Add vermouth or wine and reduce until slightly dry. Add fish stock and reduce by a third.
Add cream slowly and reduce until it is thick enough to coat the back of a spoon. Stir frequently. Add oysters and their liquor and cook until meat slightly curls at edges, about 3 minutes. Season to taste with salt, pepper, and lemon juice. Add chives. Serve immediately.
Spread a layer of sea-urchin butter across pieces of toast and serve alongside stew.