Combine hulled and quartered strawberries with 1/2 cup granulated sugar and lemon juice in a bowl. Stir gently and let macerate for 30 minutes at room temperature, allowing the strawberries to release their juices.

Transfer the macerated strawberries and their juices to a blender or food processor. Blend until smooth. You can strain it for a smoother ice cream, or leave it pulpy for more texture. Set aside.

In a large bowl, whisk together the heavy cream, whole milk, the remaining 1/4 cup granulated sugar, and 1 tsp vanilla extract until the sugar is fully dissolved.

Stir in the pureed strawberry mixture into the dairy base. Cover and refrigerate for at least 2-4 hours, or preferably overnight, to thoroughly chill the mixture.

Once chilled, churn the ice cream mixture in your ice cream maker according to the manufacturer's instructions, usually for 20-25 minutes, until it reaches a soft-serve consistency. Transfer the churned ice cream to an airtight container and freeze for at least 4-6 hours, or until firm.

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

In a large bowl, using an electric mixer, cream together the softened butter, 1/2 cup granulated sugar, and brown sugar on medium speed until light and fluffy (about 2-3 minutes).

Beat in the egg and 1 tsp vanilla extract until well combined, scraping down the sides of the bowl as needed.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a soft dough forms. Do not overmix.

Divide the dough in half, flatten each half into a disk, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes (or up to 2 days). This chilling is crucial for easier handling and to prevent spreading.

Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper.

On a lightly floured surface, roll out one disk of chilled dough to about 1/8-inch thickness. Using a 2.5-inch round cookie cutter, cut out cookies. Carefully transfer them to the prepared baking sheets, leaving about 1 inch between cookies. Gather and re-roll scraps once.

Bake for 10-12 minutes, or until the edges are set and the centers are still slightly soft. They will firm up as they cool. Let cookies cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely. Repeat with the remaining dough.

Once the cookies are completely cool and the ice cream is firm, take the ice cream out of the freezer and let it soften slightly at room temperature for 10-15 minutes, until it's scoopable but still very cold.

Take one chocolate wafer cookie, place a generous scoop (about 1/3 cup) of softened strawberry ice cream on its flat side. Top with another cookie, pressing gently to spread the ice cream to the edges.

Immediately wrap each assembled ice cream sandwich tightly in plastic wrap to prevent freezer burn and help them hold their shape.

Place the wrapped sandwiches in an airtight freezer-safe container and freeze for at least 2-4 hours, or until thoroughly firm. This ensures they are solid and easy to eat.