1. Trim Brussels sprouts; cut any large ones in half. Cook, covered, in boiling salted water in a large saucepan for 10 minutes, or until tender; drain. Return to saucepan.
2. Pare cucumbers; quarter length wise; cut in 1-inch-thick slivers. Saute in butter or margarine until tender in a medium-size saucepan; remove with a slotted spoon and add to Brussels sprouts.
3. Blend flour, pepper and instant chicken broth into butter remaining in saucepan; cook, stirring constantly, until bubbly. Stir in milk; continue cooking and stirring until sauce thickens and bubbles 3 minutes. Pour over the sprouts mixture and heat very slowly just until hot.