In a medium heatproof bowl, whisk together the eggs, granulated sugar, fresh lemon juice, and lemon zest until well combined.
Place the bowl over a saucepan of simmering water (double boiler), making sure the bottom of the bowl does not touch the water.
Cook the mixture, stirring constantly with a wooden spoon or heatproof spatula, until it thickens and reaches about 170°F (77°C) on a candy thermometer. This should take about 10-15 minutes.
Remove the bowl from heat and immediately stir in the unsalted butter pieces one at a time until fully melted and incorporated.
Strain the lemon curd through a fine-mesh sieve into a clean container to remove any cooked egg bits and zest for a smooth texture.
Allow the lemon curd to cool to room temperature, then cover and refrigerate for at least 2 hours before using.
Use the lemon muffin curd to fill or top muffins, or enjoy it as a spread.