Position a rack in the center of the oven and heat the oven to 350° F.
Line four cookies with parchment of nonstick baking liner. Using a mixer fitted with the paddle attachment, 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 of tablespoonful of the dough into 1-inch balls. Thaw overnight in a refrigerator before proceeding with recipe.
Arrange the ball 1-1/2 in apart on the prepared backing sheets. Using a lightly floured glass or measuring cup, press down lightly on the balls.
Bake one sheet at time until the cookies are puffed and crackled but still moist looking (about 11 minutes).Transfer the cookies sheets to a rack to cool about 10 minutes.
Assemble the sandwich: turn half of the cookies over so they are flat side up.
Spoon 2 tbs of Nocciolata 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.