For the cornbread dippers, prepare corn muffin mix according to package directions. Spread batter in a greased 9x9x2-inch baking pan. Bake in a 400 degree F oven about 15 minutes or until top is golden. Cool bread in pan on a wire rack for 10 minutes. Remove bread from pan; cool completely on rack. Using a long-bladed, serrated knife, cut bread into 1/2-inch slices. Cut each slice into thirds. Place in a single layer on a large, ungreased baking sheet. Bake in a 400 degree F oven for 8 to 10 minutes or until crisp and cut surfaces are golden, turning slices over after 5 minutes. Cool on a wire rack. Store in an airtight container up to 2 days. Makes 48 dippers.
Meanwhile, quarter peppers; remove stems, seeds, and membranes. Place pepper pieces, skin side up. on a foil-lined baking sheet. Bake in a 425 degree F oven for 20 to 25 minutes or until skins are blistered and dark. Wrap peppers in foil; let stand 15 minutes. Peel off skin and discard. Finely chop peppers.
Meanwhile, toss together cheese and flour in a bowl; set aside. Cook onion in hot butter in a medium saucepan until onion is tender. Stir in half-and-half. Gradually add small amounts of the cheese mixture, stirring constantly over low heat until cheese is melted. Stir in roasted peppers and jicama; heat through. Transfer mixture to a fondue pot. Place fondue pot over a fondue burner. Keep dip warm up to 2 hours.