In a large skillet, melt 2 tablespoons butter over medium heat. Add onions and sugar. Cook over medium heat for 15-20 minutes or until the onions are golden brown, stirring frequently. Stir in water and bouillon. Bring to a boil. Reduce heat; simmer, uncovered, for 5-7 minutes or until liquid has evaporated. Remove from the heat; stir in cheese.
Melt remaining butter. Place one sheet of phyllo dough on a work surface; brush with butter. Brush to distribute evenly. Repeat with a second sheet; brush with butter. Cut into 12 squares. (Keep remaining phyllo covered with plastic wrap and a damp towel to prevent drying.) Repeat three times, making 48 squares.
Press one square into a greased miniature muffin cup. Top with another square of phyllo, placing corners off center. Spoon about 1 tablespoon onion mixture into cup. Repeat with remaining phyllo squares and onion mixture. Bake at 375° for 10-15 minutes or until golden brown. Serve warm.