Preheat oven to 350 degrees and grease a 11x17-inch jelly roll pan.
Place butter, granulated sugar, brown sugar, eggs, and vanilla in a large bowl. Use a hand-held eletric mixer to beat until smooth and creamy.
In a medium bowl, whisk together flour, baking soda, and salt.Add to the butter mixture and beat on low just until the flour is incorporated.
Stir in 1 1/2 bags of the toffee bits.
Transfer a little over half of the dough to the prepared pan and use your fingers to spread it in a thin layer.
In a mixing bowl, use a hand-held electric mixer to beat the cream cheese, 1/2 cup sugar, vanilla extract, and eggs until smooth. Spread over the layer of dough.
Scatter the remaining dough over the cream cheese layer, covering it as evenly as possible.Sprinkle the remaining toffee bits over the top.
Bake for 30 to 35 minutes. Let cool completely before cutting into squares.
Notes
If you don't have unbleached flour, you can use bleached all-pupose flour.