Melt-in-Your-Mouth Peanut Butter Cookie Sandwiches

Ingredients

• 1 cup (4 1/2 oz or 128g) all purpose flour, sifted
• 1/2 cup (2 oz or (57g) cake flour, sifted
• 1/2 teaspoon baking soda
• 1/2 teaspoon fine sea salt
• 3/4 cup (6 3/4 oz or 191g) creamy peanut butter
• 1/4 cup (2 oz or 57g) unsalted butter, softened
• 1/4 cup (1 5/8 or 47g) vegetable shortening
• 1/2 cup (3 1/2 oz or 100g) packed brown sugar
• 1/2 cup (3 1/2 oz or 100g) granulated sugar, divided
• 1 large egg
• 1/2 teaspoon pure vanilla extract
• 1/2 cup (4 1/2 oz or 128g) creamy peanut butter, room temperature
• 2 tablespoons (1 oz or 28g) unsalted butter, softened
• 1/2 cup (2 oz or 57g) powdered sugar, sifted
• 2 1/2 tablespoons (1 1/4 oz or 37ml) heavy whipping cream, room temperature
• 1/4 teaspoon pure vanilla extract
• Pinch fine sea salt