Cut the butter into 1-inch cubes and allow it to soften to room temperature.
Mince the garlic, anchovy, and lemon zest (or mash in a mortar and pestle), and then fold in the butter, lemon juice, garlic chili sauce, red pepper flakes, cayenne, and salt.
Roll the butter into a log, wrap with plastic and refrigerate until needed.
Open the oysters as you would for oysters on the half shell, discarding the top shells.
Place 1-tablespoon slice of the chilled compound butter on each oyster and place on a hot grill until oysters begin to bubble and the oyster curls up around the edges, 6 to 10 minutes.
Melt a few tablespoons of butter to put on the oysters after they are grilled in case some of the butter spills out of the shells.
Serve immediately, with wedges of fresh lemon, if desired.