Make the butter (about 8 minutes). Rinse the preserved lemon under cold water, scrape out the soft pulp, and rinse the rind again. Squeeze the rind dry between paper towels and chop it finely. Mash the butter with the pulp, rind, garlic, parsley, and pepper until evenly speckled. Taste a little. It should be bright, salty, and sharply lemony.

Heat the broiler. Move a rack so it sits 6 to 8 inches (15 to 20 cm) below the heating element. Set the broiler to high, about 260°C (500°F).

Split the shells (about 8 minutes). With kitchen shears, cut lengthwise through the top shell of each tail, stopping at the tail fan. Gently loosen the meat from the shell and lift it so it rests on top, still attached at the tail end. Pat the meat dry and brush it with the olive oil.

Broil (6 to 10 minutes). Arrange the tails on a sheet pan and broil without turning. Start checking at 6 minutes. The meat is done when it turns from translucent and gray to opaque, pearly white, and firm, with light browning at the edges. One published source gives a guide of about 1 minute per ounce, another 7 to 10 minutes. Because they differ and ovens vary, trust your eyes. If a tail needs more, return it for 30 to 60 seconds at a time.

Butter and rest (1 minute). Spoon about 1 1/2 tbsp of the butter onto each tail and let it melt for a minute. The butter should slump and turn glossy, and the smell will turn sharply lemony.

Serve. Spoon the melted butter from the pan over the lobster, and serve with lemon wedges and crusty bread to mop up the rest.