Preheat the oven to 350°F (180°C). Line cookie sheets with parchment paper.

In a medium bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.

In a large bowl, beat the 1/2 cup softened butter, sugar, and lemon zest until fluffy and bright.

Beat in the egg, vanilla extract, and lemon extract until just combined.

Gradually beat in the flour mixture until a soft dough forms.

Form dough into small balls (about 1 to 1 1/2 tablespoons each) and place on prepared sheets.

Bake 9–11 minutes, until edges are set and bottoms are lightly golden.

Cool on the cookie sheet for 10 minutes, then transfer to a rack to finish cooling.

Puree the cored strawberries and strain to remove seeds.

Place the puree in a small saucepan and simmer gently until it reduces and thickens. Let it cool completely.

Beat the 3/4 cup slightly softened butter until smooth, then add powdered sugar a cup at a time, the cooled strawberry reduction, and 1/4 teaspoon salt.

Add heavy cream if needed to reach a spreadable consistency.

Spread a generous spoonful of strawberry frosting on the flat side of one cookie, then top with another to form a sandwich.

Press gently so the frosting reaches the edges.