In a food processor fitted with the S blade or in a stand mixer with the paddle attachment, combine 1½ cups flour, ½ cup + 2 tablespoons cocoa powder, 1 teaspoon baking soda, ¼ teaspoon salt, and ½ cup sugar. While pulsing or mixing on low speed, add ¾ cup butter a few pieces at a time, then add 1 egg. Continue processing until the dough comes together in a mass, about 1 minute.

Turn the dough out onto a work surface, shape into a flat disc, and wrap tightly in plastic wrap. Refrigerate for 30 minutes until firm enough to shape.

Preheat oven to 375°F and line two baking sheets with parchment paper.

Shape the cookies using one of these methods: Method 1 (Roll and Cut): On a lightly floured surface, roll the chilled dough to ⅛-inch thickness. Use a 2-inch round cookie cutter to cut circles, re-rolling scraps as needed. Transfer cut cookies to prepared baking sheets, spacing them 1 inch apart. Method 2 (Hand-Shaped): Pinch off tablespoon-sized pieces of dough and roll each into a smooth ball between your palms. Place balls on prepared baking sheets, spacing them 2 inches apart. Dampen your palm slightly and gently press each ball to flatten to ⅛-inch thickness, creating round cookies about 2 inches in diameter.

Chill the shaped cookies in the refrigerator for 10 minutes while the oven finishes preheating. This helps them hold their shape during baking.

Bake for 9 to 10 minutes, rotating the pan halfway through, until cookies are fragrant and completely set. They should look dry on top and feel firm to the touch. Let cool completely on the baking sheets before filling.

In a stand mixer fitted with the paddle attachment, beat ½ cup butter and 2½ teaspoons vanilla on medium-low speed until well combined, about 30 seconds. Scrape down the bowl.

Gradually add ½ cup powdered sugar and ⅛ teaspoon salt. Increase speed to high and beat for 2 to 3 minutes until the filling is light, fluffy, and smooth.

Using a pastry bag or small spoon, place 1 teaspoon of filling in the center of one cookie. Top with a second cookie of equal size and gently press down until the filling spreads to the edges. Repeat with remaining cookies and filling.

Serve the same day for the crispest texture, or store assembled cookies in an airtight container for up to 2 days.