Wrap garlic in foil. Roast in 450°F oven 40 minutes or until soft. Remove foil. When cool enough to handle, cut head in half horizontally. Squeeze roasted garlic pulp into food processor. Add parsley, mayonnaise, lemon juice and salt. Whirl to puree. Scrape into serving bowl.
Core, seed and split peppers. Place on broiling pan. Broil, skin side up, until blackened all over, 10 to 15 minutes. When cool enough to handle, peel skins and discard. Place peppers in food processor with sour cream and salt. Whirl until smooth puree. Scrape into a serving bowl.
Combine vegetable broth, sherry, soy sauce, brown sugar and ginger in small serving bowl.
Beat eggs, beer and salt in bowl. Gradually stir in flour until smooth. Cover; refrigerate 30 minutes.
Fill deep, heavy saucepan, wok or automatic fryer with vegetable oil to depth of several inches. Heat oil until it registers 375°F on deep-fat frying thermometer.
Dip vegetables in batter and shake off excess.
Using tongs, slotted spoon or fry basket, slip vegetables into oil, about 5 at a time. Fry, turning once, until lightly brown, 2 to 3 minutes. Remove to paper toweling to drain. Repeat with remaining vegetables. Serve dipping sauces with the vegetables.