Preheat the oven to 350°. Line a 9-by-13-inch metal baking pan with parchment paper, allowing overhang on the 2 long ends.
In a bowl, whisk the flour, baking soda and salt. In a large bowl, using a mixer, beat the butter with both sugars at medium speed until light, 1 minute. Beat in the eggs and vanilla. At low speed, beat in the dry ingredients. Stir in the chips and pretzels.
Spread the batter in the pan and top with the sprinkles. Bake for 30 minutes, until golden; the center will still be a little gooey. Transfer the pan to a rack and let cool completely.
Run the tip of a knife around the side of the pan and lift the bar out using the parchment paper. Cut into 24 squares and serve.
The bars can be stored in an airtight container at room temperature for up to 2 weeks.