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In a bowl, combine all the streusel topping ingredients. With your fingers, combine until you have a crumbly mixture. Set aside.
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Preheat the oven to 400˚ F. and line 16 muffin cups with paper liners.
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In a bowl, mix together the dry ingredients (flour, salt, baking powder and baking soda); set aside. In another bowl, combine the oil, brown sugar, and egg. Once combined, stir in the buttermilk and vanilla extract.
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Add the wet ingredients to the dry ingredients and mix well. Gently mix in the apple*. If the batter seems to thin, add a tiny bit more flour. The batter should be fairly stiff. Spoon the batter into the muffin cups dividing it equally.
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Divide the streusel topping equally among the muffins.
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Lower the temperature to 350˚ F. and bake for 20-25 minutes. When the muffins are done, they will spring back when lightly pressed. Otherwise, test the muffins by inserting a toothpick. Let the muffins cool in the pan for 10 minutes and then remove them and let cool for 15-20 minutes on a wire rack before drizzling with caramel icing.
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While muffins are baking, prepare drizzle mixture. Combine brown sugar, butter and milk in a medium size microwave-safe bowl. Microwave on high for 30 seconds, stir well and return to microwave for 15 seconds.
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Add vanilla. While stirring, add powdered sugar and mix until smooth and creamy. Mixture should drizzle easily, but should not be super 'runny". Add a bit more milk or powdered sugar to adjust thickness. Drizzle over cooled muffins.