Prepare and light a grill or preheat the oven to 500 degrees F (260 degrees C).

In a small bowl, blend together the softened butter, ground fennel seeds, minced shallots, chopped fennel greens, pepper, and salt.

Arrange the oysters on the grill or oven rack.

Cover and cook for 3 to 5 minutes, or until they start hissing and begin to open.

Using an oyster knife, pry each oyster open at the hinge.

Loosen the oyster and discard the flat shell.

Top each oyster with 1/2 teaspoon of the fennel butter.

Return to the grill and cook until the butter is melted and hot.