Place the shrimp, garlic, cayenne, and olive oil in a 9 by 9 by 2-inch baking dish and toss well; cover and marinate at least 24 hours in the refrigerator. When ready to cook, preheat the broiler. Lay the shrimp on a well-oiled broiler pan and brush generously with the marinade, and broil 2 minutes longer. Serve sizzling hot with little bowls of the dipping sauce (1 for each person). To cool the fire, accompany with a crisp green salad, chunks of good Portuguese bread and well-chilled vinho verde.
Variation: Camaroes Grelhados Piri-piri (Grilled Shrimp with Hot Red Peppers): Marinate the shrimp as directed. When ready to cook, build a hot charcoal fire and when the flames have died down, leaving white-hot coals, arrange the shrimp, not quite touching one another, on 4 to 6 well-oiled long metal skewers. Adjust the height of the grill so that it is about 6 inches above the coals, lay the skewers on the grill and cook about 6 minutes, turning often, and brushing with additional marinade. Serve with little bowls of Molho de Piri-piri.
Stem the peppers and coarsely chop (include the seeds); place in a 1-pint shaker jar along with the salt, olive oil, and vinegar. Cover tight, shake well, then store at room temperature. The sauce will keep well for about a month. Shake the sauce every time you use it.
For mellower, roast the peppers uncovered for 15 minutes at low heat (300 degrees F.)
Recipe courtesy Jean Anderson, The Food of Portugal, Hearst Books, 1986