Preheat the oven to 350°F (175°C). Lightly butter an 8x8-inch pan, line it with parchment paper leaving an overhang, and lightly butter the parchment.
In a large bowl or the bowl of a stand mixer fitted with the whisk attachment, beat the eggs, granulated sugar, packed light brown sugar, vanilla extract, salt, and baking soda on high speed for 2 to 3 minutes, until the mixture is light in color and thick but not stiff.
Reduce the mixer to low and slowly drizzle in the lukewarm melted butter, mixing until fully incorporated.
With the mixer on low, sprinkle in the all-purpose flour and mix until just combined, scraping down the bowl as needed.
Fold in about three-quarters of the chopped chocolate sandwich cookies, semisweet chips, white chocolate chips, and most of the sprinkles, reserving a little of each for the top.
Spread the batter evenly into the prepared pan. Sprinkle the reserved chopped cookies, chocolate chips, and sprinkles over the top.
Bake for 30 to 35 minutes, until the top is shiny and set and the edges begin to brown; timing can vary by oven and pan. Avoid relying on a toothpick test for moist blondies.
Remove from the oven and cool the pan on a wire rack to room temperature. For clean slices, chill for a few hours or overnight.
Use the parchment overhang to lift the blondies from the pan and cut into 16 even squares with a large chef's knife, wiping the blade between cuts.