Prepare and light a grill or preheat the oven to 500 degrees F (260 degrees C).
In a small bowl, blend together the butter, ground fennel seeds, shallots, fennel bulb, 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 grill and cook until butter is melted and hot.