Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, beat the softened butter, peanut butter, granulated sugar, and brown sugar together with an electric mixer on medium speed until creamy and smooth, about 2-3 minutes.
Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Roll the dough into 48 equal 1-inch balls and place them 2 inches apart on the prepared baking sheets.
Flatten each ball slightly with the bottom of a glass or your palm.
Bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and let the cookies cool on the baking sheets for 5 minutes.
Transfer the cookies to a wire rack to cool completely.
Once cooled, spread about 1 teaspoon of raspberry jelly on the flat side of 24 cookies.
Top each jelly-spread cookie with another cookie, flat side down, to form sandwich cookies.
Press gently to adhere and serve or store.