Prepare the lemon curd first by whisking the eggs, sugar, lemon juice, lemon zest, and salt together in a heatproof bowl until well combined.
Set the bowl over a saucepan with gently simmering water (double-boiler style) and cook, whisking constantly, until the mixture thickens enough to coat the back of a spoon, 8–10 minutes.
Remove the curd from heat, whisk in the butter pieces until smooth, then strain through a fine mesh strainer into a clean bowl.
Press plastic wrap directly onto the surface of the lemon curd and chill in the refrigerator for at least 30 minutes or until cold and thick.
Preheat your oven to 350°F (175°C) and line a 12-cup muffin pan with paper cupcake liners.
In a medium bowl, whisk together the flour, baking powder, and salt, then set aside.
In a large bowl, beat the softened butter and granulated sugar with a mixer on medium speed until pale and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition, then mix in the lemon zest and vanilla extract until combined.
In a small bowl or jug, stir together the milk and lemon juice.
Add the dry ingredients to the butter mixture in two additions, alternating with the milk mixture, beginning and ending with the dry ingredients and mixing on low just until combined.
Divide the batter evenly among the 12 liners, filling each about two-thirds full.
Bake the cupcakes for 16–18 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Let the cupcakes cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely, about 20–30 minutes.
While the cupcakes cool, make the lemon buttercream by beating the softened butter in a large bowl until creamy, about 1–2 minutes.
Gradually add the powdered sugar, starting on low speed, then beat in the lemon juice, lemon zest, salt, and 1 tablespoon of cream or milk until smooth and fluffy, adding more powdered sugar or cream to reach piping consistency.
Once the cupcakes are completely cool, use a small paring knife to cut a cone-shaped piece from the center of each cupcake, reserving the cut-out pieces.
Spoon or pipe about 1–2 teaspoons of chilled lemon curd into the cavity of each cupcake.
Trim the reserved cupcake cones to make a small “lid,” then gently place them back over the lemon curd (optional).
Transfer the lemon buttercream to a piping bag fitted with your desired tip or use a small offset spatula to frost the tops of the cupcakes.
Optionally, garnish the cupcakes with a small swirl of extra lemon curd, a pinch of lemon zest, or thin lemon slices before serving.