Combine the creme fraiche, 1/4 teaspoon of salt, and 1/2 teaspoon of the pepper in a small bowl, and mix well. Transfer to a fine-mesh strainer set over a bowl, refrigerate, and let drain for up to 2 hours. Transfer to a bowl, cover and refrigerate until needed.

Drain the oysters in a fine-mesh strainer set over a bowl. Reserve 1 1/2 cups of their liquid and refrigerate the oysters.

Melt the butter in a medium pot over medium-high heat. Add the shallots and cook, stirring, for 2 minutes. Add the heavy cream, the 1 1/2 cups oyster liquor, and the anise-flavored liqueur, and bring to a boil over medium-high heat. Add the remaining 1 teaspoon salt and 1 teaspoon black pepper, and reduce the heat to medium. Simmer until reduced by half, about 10 minutes. Remove from the heat. Add half of the spinach to the pot and puree with an immersion blender, or in batches in a blender or food processor. Strain through a fine-mesh strainer into a large clean saute pan, and keep warm.

Heat the oil in a deep, heavy pot or electric fryer to 350 degrees F.

Fry the remaining spinach in batches in the hot oil until crispy, about 45 seconds. With a slotted spoon, remove the cooked spinach and drain on paper towels. Season lightly with salt, to taste.

Add the oysters to the cream sauce and bring to a gentle simmer. Cook until the edges of the oysters start to curl, about 3 minutes. Remove from the heat.

To serve, arrange 6 oysters around the inner edge of each of 6 shallow, rimmed soup bowls (like the spokes of a wheel). Spoon 1/2 cup of sauce around the oysters in each bowl. Spoon a dollop of creme fraiche into the center of each bowl, top with a teaspoon of the Beluga caviar, and garnish with fried spinach. Serve immediately.