Preparation

Make the cookies:

• Position a rack in the center of the oven and heat the oven to 350ºF. Line four cookie sheets with parchment or nonstick baking liners.
• In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl with a hand mixer), beat the peanut butter, brown sugar, and baking soda on medium speed until well blended, about 1 minute. Add the eggs and vanilla and mix on low speed until just blended, about 25 seconds.
• Shape level tablespoonfuls of the dough into balls about 1 inch in diameter. Arrange the balls 1-1/2 inches apart on the prepared baking sheets. Do not press down. Bake one sheet at a time until the cookies are puffed and crackled but still moist-looking, about 11 minutes. Transfer the cookie sheet to a rack to cool about 10 minutes. Using a spatula, move the cookies to the rack and let cool completely. Repeat with the remaining cookies.

Make the filling:

• Melt the chocolate and the butter in the microwave or in a medium heatproof bowl set in a skillet with 1 inch of barely simmering water, stirring with a rubber spatula until smooth. Remove from the heat and set aside until cool and slightly thickened, 20 to 30 minutes.

Assemble the sandwiches:

• Turn half of the cooled cookies over so they are flat side up. Spoon 2 tsp. of the chocolate filling onto the center of each cookie. Top with the remaining cookies, flat side down. Press gently on each cookie to spread the filling almost to the edge. Set on the rack until the filling is firm, 20 to 30 minutes.

Make Ahead Tips

The balls of dough may be frozen before baking for 1 month. Thaw them overnight in the refrigerator before proceeding with the recipe.