Add the peanut butter, butter and shortening to the bowl of a standing mixer fitted with a paddle attachment, and beat together. Add the brown sugar, and cream until light and fluffy, about 6 minutes. Add the eggs, one at a time, beating well in between each addition. Beat in the vanilla and combine until mixed.
Whisk the flour, baking soda and 3/4 teaspoon salt together in a medium bowl. Add the flour in 3 additions to the peanut butter mixture, beating until just combined. Stir in the peanut butter chips.
Use a 1/2-cup ice cream scoop and scoop the cookie batter onto one of the prepared sheet trays. Gently press down the tops of the cookies with a fork making a criss-cross. Sprinkle each cookie with a small pinch of salt and sugar. Place in the refrigerator to firm up, at least 30 minutes.
Preheat the oven to 375 degrees F.
Place 6 firmed cookies on each prepared sheet tray, leaving at least 4 inches of space between the cookies. Bake in batches until golden, 18 minutes, rotating the pans halfway through baking.