Step 1

Thaw 1 (8-ounce) container frozen whipped topping if needed. Let 8 ounces cream cheese sit at room temperature until softened, about 45 minutes. Line the bottom and sides of an 8x8-inch baking pan with 2 sheets of parchment paper, positioning them perpendicular to each other and making sure they are long enough to hang over all four sides by at least 1 inch to form a sling.

Step 2

Place 4 tablespoons unsalted butter in a large microwave-safe bowl. Microwave on HIGH until melted, 40 to 60 seconds. (Alternatively, melt the butter on the stovetop.)

Step 3

Break 8 ounces shortbread cookies into large pieces and place in the bowl of a food processor fitted with the blade attachment. Pulse until fine crumbs form, 15 to 20 (1-second) pulses; you should have about 1 1/2 cups crumbs. (Alternatively, place the cookies in a sealed zip-top bag and crush with a rolling pin into fine crumbs.)

Step 4

Drizzle the butter over the cookie crumbs (reserve the bowl). Add 1/4 teaspoon of the kosher salt. Pulse until it resembles wet sand and holds together when squeezed, about 7 (1-second) pulses. (If making by hand, transfer the crumbs to a medium bowl and add the melted butter and salt. Stir until the mixture resembles wet sand and holds together when squeezed.)

Step 5

Transfer the mixture into the baking pan. Use the bottom of a measuring cup or your fingers to press the crumbs into an even layer, making sure to reach the edges and fill the corners. Wash and dry the food processor bowl, blade, and lid.

Step 6

Finely grate the zest from 1 medium lemon (about 1 tablespoon) and juice the lemon until you have 2 tablespoons; place both into the food processor. Add the cream cheese, 1 cup powdered sugar, and the remaining 1/4 teaspoon kosher salt. Process until very smooth and lightened in texture, about 1 minute.

Step 7

Transfer half of the cream cheese mixture (about 1/3 cup) into the reserved butter bowl (leave the remaining in the food processor), add 1 cup of the whipped topping, and fold with a flexible spatula until combined. Dollop over the crust and spread into an even layer.

Step 8

Place 1 (0.8- to 1.2-ounce) package freeze-dried strawberries in a plastic zip-top bag, press the air out, and seal. Crush with a rolling pin until finely ground into a powder. Transfer 2 tablespoons of the strawberry powder to an airtight container and set aside at room temperature until ready to serve.

Step 9

Add the remaining strawberry powder and 1/2 cup strawberry preserves to the food processor and process until very smooth, 30 seconds to 1 minute. Transfer to the reserved butter bowl, add 1/2 cup of the whipped topping, and fold until just combined. Dollop over the lemon filling and spread into an even layer.

Step 10

Dollop the remaining whipped topping (about 1 1/2 cups) over the top of the strawberry filling and spread into an even layer. Cover with plastic wrap and refrigerate until firm, at least 4 hours or up to overnight.

Step 11

Grasping the excess parchment paper, lift the slab out of the pan and place on a cutting board or serving platter. Place the reserved strawberry powder in a fine-mesh strainer and dust over the top of the bars. Cut into 9 bars, wiping the knife clean after each slice to maintain the layered appearance.