MAKE THE COOKIES
Heat oven to 375 and line two cookie sheets with parchment paper
Place the butter in a bowl of a stand mixer with paddle attachment and beat on medium for 2 minutes. Alternatively, use a medium bowl and hand mixer and do the same.
Add the sugar and beat for another 2 minutes, scraping down the sides as needed. Add the egg and the vanilla, mixing for another 30 seconds.
Add the flour, baking powder and salt and beat on low for 1 1/2 to 2 minutes, or just until the dough comes together to form a ball.
Turn the dough out to a lightly floured surface and divide in half. Working with one half at a time, pat the dough into disc with the palm of your hand then roll it out with a rolling pin to 1/4 inch of thickness. Using a 3" round cutter, cut the dough and gently lift and place on prepared baking sheets. Repeat with other portion of dough, pressing any leftover dough scraps together and rolling them out for cutting too, in order to use all the dough. Refrigerate on the sheets for 20 minutes. Remove from fridge and bake for 10-14 minutes until golden brown on the edges. Cool on a baking sheet for 10 minutes before transferring to a wire rack to cool completely.
MAKE THE FROSTING
Beat the cream cheese in a large bowl with a hand mixer until light, about 2 minutes.
Add lemon zest, salt and vanilla and beat until combined.
Add powdered sugar and mix until combined and free of lumps.
The frosting should be thick, so add more powdered sugar if needed. Refrigerate for 30 minutes.
PREPARE THE STRAWBERRIES
Place the jam in a small bowl and add 1/2 teaspoon of water to loosen it up.
Pour jam over strawberries and lightly toss everything to coat.
TO ASSEMBLE COOKIES
Using completely cooled cookies, frost each cookie with one generous tablespoon of frosting, and top with 1 1/2 tablespoons of the strawberry mixture.
Store the unfrosted cookies in an airtight container for up to 4 days. Cookies are best assembled right before eating.