Place beef liver in medium bowl; add milk. Cover and refrigerate 30 minutes.

Preheat broiler. Remove liver from milk; discard milk. Place liver on rack in foil-lined broiler pan so surface of beef is 3 to 4 inches from heat. Broil 9 to 12 minutes until instant-read thermometer inserted horizontally into center registers 160°F, turning once.

Place liver in food processor bowl. Pulse on and off until finely chopped; remove liver from processor. Add egg, onion and garlic to food processor; pulse on and off until paste forms. Return liver to food processor; add lard. Pulse on and off until blended. Add parsley; pulse until mixture is smooth is smooth. Season with salt and pepper, as desired.

Place liver mixture into medium bowl; cover and refrigerate for at least 1 hour.