Grind the rolled oats into a fine consistency using a food processor or coffee grinder. This will ensure they blend easily into the batter.
In a bowl, whisk together the flour, ground oats, baking powder, and vanilla sugar.
Cream the softened butter and sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition.
Grate the orange zest into the mixture. Squeeze the orange juice and add it to the butter and egg mixture.
Gradually add the dry ingredients to the wet ingredients, then pour in the milk. Mix until just combined; do not overmix.
Line a muffin tin with paper liners, then evenly spoon the batter into each cup.
Bake in a preheated oven at 350°F (180°C) for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin before serving. Dust with powdered sugar or drizzle with orange glaze if desired.
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