Bring a large pot of salted water to a boil. Add potatoes and cook until tender but still firm, about 15 to 20 minutes. Drain and cool. Peel potatoes and slice 1/4 inch thick; set aside.
Heat oil in a medium-size skillet; saute onion until soft. Stir in flour, mustard, celery seed and salt. Gradually add water and vinegar; cook over low heat, stirring constantly, until mixture boils and thickens.
In a mixing bowl, combine the potatoes, green pepper, carrots and dill; add sauce and mix well. Spoon half the mixture into a shallow 8×8 inch baking dish and sprinkle with half the cheese. Cover with remaining potato mixture and cheese.
Bake uncovered at 350 degrees F (175 degrees C) for 15 to 20 minutes, or until cheese is melted and vegetables are heated through.