Preheat the oven to 375 degrees F (190 degrees C). Line a 12-cup muffin pan with paper liners or lightly grease the cups.
In a large bowl, whisk together the flour, sugar, baking powder, and salt.
In a separate bowl, whisk the melted butter, eggs, milk, lemon zest, lemon juice, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir just until combined. Do not overmix.
Spoon about 1 tablespoon of batter into each muffin cup. Add 1 teaspoon of cold lemon curd to the center of each, then top with the remaining batter until the cups are about three-quarters full, spreading gently to seal in the curd completely.
Bake for 18 to 22 minutes, until the tops are set and lightly golden. A toothpick inserted into the muffin, avoiding the curd center, should come out mostly clean.
Cool the muffins in the pan for 5 minutes, then transfer to a wire rack to cool completely.