Preheat oven to 370 degrees Fahrenheit. Line a 9x9 inch baking pan with aluminum foil and spray with non-stick cooking spray. Set aside.
Whisk together the 2 ¼ cups all-purpose flour, 1 teaspoon baking soda, and ½ teaspoon salt in a medium-sized bowl. Set aside.
In a large bowl, using an electric or stand mixer, whisk together the ¾ cup softened unsalted butter, ½ cup granulated sugar, l¾ cup packed light brown sugar, and 1 tablespoon vanilla extract until light and creamy.
Add the 2 large eggs one at a time, mixing well between each egg.
Add the flour mixture to the butter mixture and mix until just combined. Be careful not to overmix.
Using a spatula, stir in 1 ½ cups white chocolate chips until combined.
Press dough into the prepared baking pan. Bake for 20-23 minutes or until the edges are lightly golden brown. Top with additional chocolate chips, and let the bars cool completely before cutting into squares.