Move an oven rack to the center position and preheat the oven to 350°F (175°C). Lightly spray a 9x13-inch baking pan with nonstick cooking spray, line with parchment paper leaving 2 inches hanging over the long sides, and spray the parchment lightly.
Measure ¾ cup of pure pumpkin puree, spread it over a plate lined with a double layer of paper towels, and press another paper towel gently on top to blot for about 30 seconds. Scrape the blotted puree into a small bowl and set aside.
In a medium bowl, whisk together the flour, pumpkin pie spice, baking powder, and fine salt for about 30 seconds until evenly combined. Set aside.
Melt the butter in the microwave in 20-second bursts or in a small saucepan over low heat, then let it cool for about 5 minutes until warm but not hot. Pour into a large mixing bowl, add the brown sugar, and whisk for about 1 minute until smooth and glossy.
Add the whole egg and egg yolk to the butter mixture and whisk until fully combined. Stir in the vanilla extract, then add the blotted pumpkin puree and whisk until smooth and evenly colored with no streaks.
Pour the flour mixture over the wet mixture and fold gently with a silicone spatula until only a few streaks of flour remain. Reserve ¼ cup of white chocolate chips for the topping, then fold in the remaining 1¼ cups until the flour disappears and the chips are evenly spread.
Scrape the batter into the prepared pan and press into an even layer reaching all four corners using a dampened spatula or fingertips. Scatter the reserved ¼ cup of white chocolate chips over the top and sprinkle with a small pinch of flaky sea salt if desired.
Bake on the center rack for 30 to 35 minutes, checking at 30 minutes. The edges should be set and golden brown and the center should look matte with just a slight wobble; a toothpick should come out with a few moist crumbs, not wet batter. If the chips brown too fast, loosely cover with foil for the last few minutes.
Set the pan on a wire cooling rack and let the blondies cool for at least 1 hour. Use the parchment handles to lift the slab onto a cutting board, then cut into 4 rows by 6 rows to make 24 squares, wiping the knife clean between cuts.