In a medium saucepan, combine the raspberries and granulated sugar. Cook over medium heat, stirring occasionally, until the raspberries break down and the mixture becomes juicy, about 5 to 7 minutes. Mash the berries with the back of a spoon to help them break down.

In a small bowl, whisk together the cornstarch and cold water until smooth to create a slurry. Pour this slurry into the saucepan with the raspberry mixture. Continue to cook, stirring constantly, until the filling thickens enough to coat the back of a spoon, about 2 to 3 minutes more.

Remove the saucepan from the heat and stir in the lemon juice. For a seedless filling, you can press the mixture through a fine mesh sieve. Transfer the filling to a bowl and let it cool completely to room temperature, then chill in the refrigerator for at least 30 minutes to an hour to firm up.

Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper. In a medium bowl, whisk together the all purpose flour, unsweetened cocoa powder, baking soda, and salt. Set this dry mixture aside.

In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a hand mixer, beat the softened butter, granulated sugar, and brown sugar on medium high speed until the mixture is light, creamy, and pale, about 3 to 4 minutes.

Add the eggs one at a time, beating well after each addition and scraping down the sides of the bowl as needed. Beat in the vanilla extract until combined.

Reduce the mixer speed to low and gradually add the dry ingredient mixture to the wet ingredients. Mix until just combined. Be careful not to overmix; stop as soon as you no longer see streaks of flour. The dough will be soft.

Using a small cookie scoop (about 1 tablespoon), drop rounded spoonfuls of dough onto the prepared baking sheets, spacing them about 2 inches apart.

Bake for 10 to 12 minutes, or until the edges are set and the centers look soft. The cookies will look slightly underbaked, which is key to a chewy texture. Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.

Once the cookies are completely cool, find pairs of similarly sized cookies. Spread or pipe about 1 to 2 teaspoons of the chilled raspberry filling onto the flat side of one cookie. Gently press a second cookie on top to create a sandwich. Repeat with the remaining cookies and filling.