Cut the melon flesh into chunks, and discard the rind.
Place the chunks in a large saucepan over medium heat for 2 to 3 hours, stirring occasionally, or until the melon is the consistency of applesauce.
Stir in the tomato paste, onion powder, garlic powder, brown sugar, sherry, lemon juice, and liquid smoke. Reduce heat to low, and simmer uncovered for 2 hours. Allow mixture to cool to room temperature before using.
