In a large saucepan, heat the oil. Add the onion and minced garlic; cook over moderate heat until softened, 5 minutes.
Add the vermouth; boil over moderately high heat until reduced by half, about 2 minutes. Add the oyster liquor and fish stock and simmer for 3 minutes.
Add the cream and simmer over moderate heat until the sauce coats a spoon, 5 minutes. Remove from the heat. Add 1 teaspoon of the lemon juice; season with salt.
Meanwhile whisk the uni tongues and softened butter together to make the Uni Butter.
Add the oysters to the sauce with a little oyster liquid and butter. Add the tarragon and remaining lemon juice and cook over moderately low heat until warmed through, 2 minutes.
Divide the oysters among 4 bowls, add sauce and sprinkle with the cayenne pepper. Serve with the toasts that have been spread with the Uni Butter.