Parboil perogies in a 6 to 8 quart pot of boiling salted water, uncovered, stirring occasionally, 1 minute less than package instructions indicate (perogies will not be completely cooked) Transfer with a slotted spoon to a colander to drain. Pat dry.
Heat 1 TBS oil in a 12 inch heavy skillet and saute half of the perogies, turning over once, until golden, about 4 minutes per batch. Transfer to a large platter and cover loosely with foil. Keep warm. Add 1 TBS oil to skillet and cook remaining perogies in same manner.
Cook bacon in same skillet over moderately high heat stirring occasionally until crisp and golden, 6 to 8 minutes, then transfer to paper towels to drain. Pour off all but 1 TBS of fat from skillet, then add remaining oil and saute onion, stirring until golden, about 8 minutes.
Reduce heat to moderate, then stir in garlic, cabbage, water and salt. Cook, covered, stirring occasionally until cabbage is tender, 5 to 7 minutes. Transfer to platter with perogies and sprinkle with bacon and dill.