Preheat oven to 350°. Line muffin pan with liners (about 16).
Stir oil, yogurt, and peanut butter with a wooden spoon. Stir in both sugars.
Add the eggs, vanilla, baking soda, and baking powder and stir until combined.
Add half the flour and half the milk and stir until just mixed. Add the rest of the flour and milk and stir until the batter just comes together. Stir in the chopped Cadbury eggs.
Add about 3/4-1 cup of batter per muffin cup (I use an ice cream scoop for this step). They won’t rise much, so you can fill them almost full. Press 1 or 2 Cadbury eggs in the top of each muffin. Bake about 15-20 minutes, removing from oven when a toothpick inserted in the side of the muffin comes out clean.