In a medium heatproof bowl, whisk together the eggs, granulated sugar, fresh lemon juice, and lemon zest until fully combined.
Place the bowl over a saucepan of simmering water, making sure the bottom of the bowl does not touch the water.
Cook the mixture, stirring constantly with a whisk or wooden spoon, until it thickens and coats the back of a spoon, about 10 to 15 minutes.
Remove the bowl from heat and immediately stir in the unsalted butter pieces until fully melted and incorporated.
Strain the lemon curd through a fine mesh sieve into a clean container to remove zest and any cooked egg bits for a smooth texture.
Allow the lemon curd to cool to room temperature, then cover and refrigerate until chilled and set, at least 2 hours before using.
Use the lemon curd to fill or top muffins, or enjoy as a spread.