In the bowl of a stand mixer fitted with the paddle attachment, beat butter, 1/2 cup granulated sugar, and brown sugar at medium speed until fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Add egg and egg yolk, beating well. Add peanut butter and vanilla bean paste, beating until combined.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined. Using a 1 1/2-tablespoon spring-loaded scoop, scoop dough into mounds and place on prepared pan. Refrigerate for 30 minutes.
Preheat oven to 350. Line 2 baking sheets with parchment paper. Place remaining 1/2 cup granulated sugar in a small bowl. Roll each mound into a ball, and roll balls in sugar, coating completely. Place 2 1/2 inches apart on prepared pans. Press tines of a fork into each ball, making a crosshatch design.
Bake until light golden brown, 10 to 12 minutes, rotating pans halfway through baking. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on wire racks.
Place Peanut Butter Mousse in a piping bag fitted with a 1/2-inch round piping tip (Ateco #805). Pipe Peanut Butter Mousse onto flat side of half of cookies. Spoon about 1 teaspoon jelly onto flat side of remaining cookies. Sandwich together peanut butter cookies and jelly cookies. Refrigerate until filling is set, about 30 minutes. Cover and refrigerate for up to 3 days.
*We used JIF Natural Creamy Peanut Butter
Peanut Butter Mousse
In the bowl of a stand mixer fitted with paddle attachment, beat butter and cream cheese at medium speed until smooth. Beat in peanut butter. Gradually add confectioners' sugar in two additions alternately with cream, beating until smooth. Use immediately.