Preheat oven to 350°F. Line 2 large baking sheets with parchment paper and set aside.
Make the chocolate dough: In a medium bowl, whisk together 1 cup (125 g) flour, cocoa powder, ½ teaspoon baking soda, ¼ teaspoon salt, and espresso powder; set aside.
In a large bowl, beat ½ cup softened butter, ½ cup granulated sugar, and ½ cup brown sugar with a mixer on medium speed until light and fluffy, about 2 minutes.
Add 1 egg and 1 teaspoon vanilla bean paste to the chocolate dough butter mixture and beat until smooth.
Add the dry chocolate mixture to the wet ingredients and mix on low just until combined and no dry streaks remain; set chocolate dough aside.
Make the pink dough: In a separate bowl, whisk together 1½ cups (190 g) flour, ½ teaspoon baking soda, and ¼ teaspoon salt; set aside.
In a clean large bowl, beat remaining ½ cup softened butter, ½ cup granulated sugar, and ½ cup brown sugar until light and creamy, about 2 minutes.
Add remaining 1 egg and 1 teaspoon vanilla bean paste to the pink dough butter mixture and beat until smooth.
Add the dry pink dough mixture and mix on low just until combined, then mix in freeze-dried raspberry powder or pink food coloring until the dough is evenly tinted.
Scoop small portions of chocolate dough and pink dough (about 1 tablespoon of each), press them gently together, and roll into 1½-inch balls with marbled colors.
Arrange the dough balls on prepared baking sheets, spacing them about 2 inches apart.
Bake cookies at 350°F for 10–12 minutes, until the edges are set and the centers look puffy but still soft.
Let cookies cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely before filling.
While cookies cool, make the ganache: Place the chopped chocolate or chocolate chips in a heatproof bowl.
Warm the heavy cream in a small saucepan over low heat until steaming around the edges but not boiling.
Pour the hot cream over the chocolate, let sit for 1 minute, then stir slowly until smooth and glossy; stir in 1 tablespoon butter if using.
Let the ganache sit at room temperature, stirring occasionally, until thickened to a spreadable consistency similar to soft peanut butter.
Sort cooled cookies into pairs of similar size. Turn one cookie in each pair flat-side up and spread or pipe about 1 tablespoon of ganache onto the center.
Top with the second cookie, flat-side down, and gently press to spread the ganache to the edges, creating a sandwich.
Decorate the tops with crushed freeze-dried raspberries, chocolate square pieces, heart sprinkles, and a drizzle of melted white chocolate. Let the ganache set before serving.