Melt butter in a Dutch oven over medium heat. Add potato and next 4 ingredients. Cover and cook over medium heat, stirring occasionally, 10 minutes (do not brown).
Whisk together 1/2 cup clam juice and flour in a small bowl; add to vegetables, stirring gently. Stir in remaining clam juice. Bring to a boil; reduce heat, and simmer, uncovered, 25 minutes or until vegetables are tender. Stir in clams and half-and-half.