Peanut Butter Lunch Lady Cookie Bars

Ingredients

• 2 cups flour
• 2 cups sugar
• 2 large eggs, beaten
• 1 ½ cup peanut butter, divided
• 1 ½ cups (3 sticks) unsalted butter, softened
• ½ cup milk + 2 tablespoons, divided
• 1 teaspoon baking soda
• 1 teaspoon vanilla extract
• 1 teaspoon salt
• 4 cups powdered sugar