Sprinkle sugar in an even layer in a large, heavy saucepan.
Combine 2/3 cup water and syrup; pour over sugar. Cook over medium-high heat until sugar dissolves (about 4 minutes), stirring gently. Cook an additional 20 minutes or until golden (do not stir).
Remove from heat. Gradually stir in milk, half-and-half, and butter using a long-handled wooden spoon (mixture will bubble vigorously). Cook over low heat until mixture is smooth, stirring constantly.