Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In a separate medium bowl, whisk the melted butter, buttermilk, eggs, lemon zest, lemon juice, and vanilla extract until combined.
Pour the wet ingredients into the dry ingredients and gently fold together until just combined. Do not overmix; the batter should be slightly lumpy.
Fill each muffin cup about halfway with batter.
Prepare the lemon curd: In a medium heatproof bowl, whisk together the eggs, sugar, lemon juice, and lemon zest until smooth.
Place the bowl over a saucepan of simmering water (double boiler method), making sure the bottom of the bowl does not touch the water.
Add the butter pieces and cook, whisking constantly, until the mixture thickens and reaches about 170°F (77°C), about 8-10 minutes. The curd should coat the back of a spoon.
Remove the lemon curd from heat and let it cool slightly.
Spoon about 1 teaspoon of lemon curd onto the center of each muffin cup over the batter.
Top each muffin cup with the remaining batter, covering the lemon curd completely.
Bake for 18-20 minutes, or until a toothpick inserted near the edge (not in the curd) comes out clean and the muffins are golden.
Let the muffins cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
Serve the muffins warm or at room temperature. Optionally, dust with powdered sugar before serving.