Beat 1/3 cup peanut butter and sugar at medium speed with an electric mixer until creamy. Add eggs, beating until blended.
Stir together flour, cocoa, baking soda, and salt; add to peanut butter mixture, beating at low speed until blended. Turn dough out onto a lightly floured surface; knead in peanuts and 1/2 cup chocolate mini-morsels.
Shape dough into a 13" x 3" log on a lightly greased baking sheet. Bake at 325° for 40 minutes or until firm. Remove to a wire rack to cool (about 20 minutes).
Cut log diagonally into 1/2"-thick slices with a serrated knife, using a gentle sawing motion; place slices on ungreased baking sheets. Bake at 325° for 7 minutes; turn cookies over, and bake 7 more minutes. Remove to wire racks to cool.
Combine remaining 1 cup chocolate mini-morsels, 1 1/2 tablespoons peanut butter, and shortening in a small saucepan. Cook over low heat until chocolate and peanut butter melt. Dip one end of each biscotti in chocolate mixture. Place biscotti on wax paper until chocolate hardens.