In your mixing bowl, beat the softened unsalted butter and powdered sugar together on medium speed until light, fluffy, and pale, about 3-4 minutes.
Add the two large eggs one at a time, beating well after each addition. Then add vanilla extract and mix until combined and smooth.
In a separate bowl, whisk together all-purpose flour, salt, and freshly grated lemon zest. Gradually add this dry mixture to the wet ingredients, mixing on low speed just until dough forms. Avoid overmixing.
Cover the dough with plastic wrap and refrigerate for at least 30 minutes to firm up.
Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper or silicone mat. Portion dough into 1-inch balls using a small cookie scoop or spoon. Roll each ball in granulated sugar.
Place dough balls on baking sheet about 2 inches apart. Use your thumb or back of a teaspoon to create an indentation in the center of each ball. Fill each indentation with about 1/2 teaspoon lemon curd without overfilling.
Bake cookies for 12-14 minutes until edges are lightly golden and centers are set but soft. Watch carefully to avoid overbaking.
Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely so lemon curd sets slightly.