Combine buttermilk and oats in a large bowl and let stand for 1 hour.
Preheat oven to 375°F (190°C). Line a twelve-cup muffin pan or 24-cup mini muffin pan with cupcake papers.
Crack the egg into the oat mixture; add sugar and beat with a whisk to combine. Whisk in melted butter.
Sift flour, baking powder, baking soda, salt, cinnamon and nutmeg into the bowl. Gently fold into batter, taking care not to overmix.
Sprinkle grated carrot and cranberries into the bowl and combine muffin batter gently but thoroughly. Use a large ice cream scoop or 1/3-cup (75 mL) measuring cup to scoop batter into muffin tins.
Bake until light brown and tops spring back when gently touched, 12 to 14 minutes. Cool in pans for a few minutes, then transfer muffins to a rack to cool completely.