In a small bowl, combine all the ingredients for the filling and stir well. It should have a crumbly consistency, but still hold together when pressed. Once everything is fully incorporated, set aside.
In your mixer, cream together the butter, peanut butter, and both sugars. Mix in the yogurt, nondairy milk, and vanilla, and continue beating until smooth. In a separate bowl, combine the flour, cocoa powder, baking soda, and salt. Slowly add these dry ingredients into the wet, being careful not to overmix.
The dough may be rather sticky at first. If you have trouble shaping it, let it rest in the refrigerator for about 30 minutes, or try moistening your hands slightly before handling.
For each cookie, roll about a tablespoon of dough into a ball and press it down flat onto your silicone baking mat or parchment paper. Line the cookies up 3 x 3 on your two baking sheets, with plenty of room in between. Drop a rounded teaspoon or so of your peanut butter filling into the center of each, and top with another flattened round of dough. Be sure to cover the whole dollop of filling, pressing the edges together, making sure that the two pieces form a complete seal all around the cookie.