Line 12 cups (each 2 1/2 inches wide) of a standard muffin tin with paper liners; set aside. In a large bowl, stir together flour, sugar, pumpkin-pie spice, baking powder, baking soda, and salt; set aside.
In a separate bowl, whisk together yogurt, butter, and egg. Make a well in the center of the dry ingredients and add yogurt mixture. Stir until just combined. Fold in carrots.
Spoon batter into prepared muffin cups. (If desired, muffins can be baked immediately in a 375-degree oven for about 20 minutes.) Freeze until firm, about 30 minutes, then cover tin with plastic wrap, and freeze until ready to bake, up to 3 months.
Preheat oven to 375 degrees. Bake muffins (still frozen) until a toothpick inserted in center of one comes out clean, about 30 minutes. Transfer to a rack. Serve warm or at room temperature.
The batter goes in the paper-lined muffin tin, then into the freezer. Once frozen, the individual cups can be transferred to plastic storage bags. Be sure to bake the batter in a muffin tin, though, to give the muffins shape.