Heat oven to 400 degrees. Grease bottoms of 12 muffin cups or line with baking cups. In medium bowl, stir together flour, 3/4 cup sugar, baking powder, and baking soda. With pastry blender, cut in butter until mixture is crumbly. Stir in strawberries.
In small bowl, whisk together buttermilk and egg until blended. Gently stir buttermilk mixture into flour mixture just until combined. Divide equally among muffin cups.
Dip cream cheese pieces in 2 tablespoons sugar, place in center of each muffin. Press cream cheese until level with batter. (Do not cover cream cheese with batter.) Sprinkle muffins with remaining 1 tablespoon sugar.
Bake 20 to 25 minutes or until light brown and toothpick inserted off center comes out clean (do not put toothpick in cream cheese.) Cool on wire rack 10 minutes. Remove from pan, serve warm or at room temperature. Store in refrigerator. Makes 12 muffins.