FOR STREUSEL: Stir brown sugar, flour, and cinnamon in small bowl. Cut in butter with a pastry blender. Set aside.
FOR MUFFINS: Lightly oil twelve 2 1/2-inch muffin cups or line with paper baking cups; set aside. In a medium mixing bowl stir together flour, granulated sugar, baking powder, and salt. Make a well in the center. In a small mixing bowl combine egg, apple cider, and oil; add all at once to flour mixture. Stir just till moistened. (The batter should be lumpy.).
Spoon about 1 tablespoon of the batter into each prepared muffin cup. Sprinkle 1 teaspoon of the brown sugar mixture over each. Fill with remaining batter. Sprinkle tops of muffins with remaining streusel.
Bake in a preheated 400° F oven until golden brown, about 20 minutes. Remove muffins from pans; cool slightly on racks.