Preheat the oven to 400 degrees F (200 degrees C). Grease 15 muffin cups or line cups with paper liners.

Beat sugar and butter together in a bowl with an electric mixer until smooth; beat in milk, egg, and vanilla extract until well blended. Combine 1 3/4 cups flour, baking powder, and salt in a separate bowl; stir into batter until just moistened. Toss huckleberries with 1 tablespoon flour in a bowl to coat: fold into batter.

Divide batter among the prepared muffin cups, filling each 2/3 full.

Bake in the preheated oven until tops spring back when lightly pressed, about 15 minutes.