Position oven racks in the upper and lower thirds of the oven and preheat to 375 degrees F. Line 2 baking sheets with parchment.
For the cookie dough: Whisk together the flour, salt and baking soda in a medium bowl.
Beat the granulated sugar and butter in a large bowl with an electric mixer on medium speed until light and fluffy, about 3 minutes. Beat in the egg until combined. Beat in the peanut butter and vanilla until smooth and creamy. Add the flour mixture and mix on low until well combined.
For the add-ins: Stir in the toffee bits with a wooden spoon until just combined.
For the filling: Scoop 2 level tablespoons cookie dough into the palm of your hand and flatten into a 2-inch round. Stack 3 chocolate rectangles in the center of the round, then top with 1 additional level tablespoon cookie dough. Press and mold the cookie dough so that it completely covers the chocolate. Flatten the cookie slightly so it is about 1 inch tall. Repeat with the remaining cookie dough and chocolate rectangles to make about 14 cookies total (you will have leftover chocolate pieces). Divide the cookies between the prepared baking sheets.
Bake, rotating the baking sheets top to bottom and front to back halfway through cooking, until the tops are puffed and the undersides are lightly browned, about 14 minutes. Cool the cookies on the baking sheets set over cooling racks for 5 minutes. Lightly dust the tops of the cookies with confectioners' sugar, then serve while still warm.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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