Preheat oven to 400 degrees F (200 degrees C). Lightly grease muffin cups or line with muffin liners.
Mix together 1/2 cup sugar, 1/3 cup flour, 1/4 cup butter, cinnamon in a small bowl with a fork until mixture resembles a coarse crumb.
Combine 1 1/2 cups flour, 3/4 cup sugar, and baking powder in a bowl. Place applesauce into a 1 cup measuring cup; add egg and enough milk to fill cup; mix into flour mixture. Fold in blueberries. Fill muffin cups to the top, and sprinkle with crumb topping mixture.
Bake in the preheated oven until golden and the tops spring back when lightly pressed, 20 to 25 minutes.
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