In a small bowl, combine the butter, anchovy fillets, garlic, Dijon mustard, Tabasco sauce, Worcestershire sauce, salt, and minced red chili pepper. Using a small fork, mash the ingredients together.
Place the shrimp in a single layer on a large baking sheet. Curl the shrimp. Scoop the compound butter mixture with a 1/4 teaspoon and place one (heaping) scoop on each curled shrimp.
Pre-heat the broiler on high for 5 minutes.
Broil the shrimp on the second-highest rack, without flipping, about 6 inches from the broiler heating element, for about 5 minutes, until they turn pink and cooked through. After 2 minutes, once the butter has melted, baste the shrimp with the melted butter.
Transfer to a serving platter, sprinkle with parsley and serve immediately.