Brown butter is enhanced with red onion, lemon, and fresh herbs to make a flavorful condiment for briny flame-kissed oysters.
Melt butter in a small saucepan over medium heat; simmer, swirling occasionally, until it turns a nutty, golden brown and dark-brown bits form on bottom of pan, 8 to 10 minutes. Remove from heat; add onion and zest. Let cool slightly; stir in parsley, chives, and lemon juice. Keep warm until ready to serve, or transfer to an airtight container and refrigerate up to 5 days. Remelt over low heat or on grill before serving.
Preheat grill for direct-heat cooking. Place oysters on grate in a single layer, curved-sides down. Cook, uncovered, just until shells open slightly, 5 to 7 minutes. (Or place on a rimmed baking sheet and put under the broiler until they pop open, 3 to 5 minutes.) Carefully transfer to a platter with tongs (don't let oyster liquor spill). When cool enough to handle, remove top shells. Spoon 1 teaspoon butter mixture into each; serve.
To ensure fresh oysters, buy them no more than one day ahead and store them on ice, uncovered, in the coldest part of the refrigerator.