Melt butter in a 2-quart pan over medium heat.
Cook onion and garlic, stirring occasionally, until golden.
Add tomatoes (break up with a spoon), basil, oregano, and pepper.
Heat to simmering.
Meanwhile, combine Longhorn and Parmesan cheeses with cornstarch.
Reduce heat to low and add cheese mixture, a handful at a time, stirring until cheeses are melted and blended.
Transfer to fondue pot or chafing dish and keep warm over heat source.
Serve with bread and vegetables for dipping.