Preheat the oven to 300 degrees F. Coat a parchment-lined baking sheet with the olive oil.
Cut a 10-inch circle in the top of the pumpkin and remove the top. Scrape out the pulp and seeds with a large spoon and remove to a bowl. Separate the seeds from the stringy pulp, then rinse the seeds in a colander under cold water. Shake the seeds dry; don't blot them with paper towels--they will stick.
Spread the seeds in a single layer on the prepared baking sheet and bake until beginning to dry out, about 30 minutes.
Meanwhile, put the bourbon in a small saucepan, set over high heat and cook until reduced slightly, 1 to 2 minutes. Add the maple syrup and cook until slightly thickened and reduced to about 1/4 cup, another 3 to 5 minutes.
Whisk the egg white in a medium bowl until foamy. Add the baked pumpkin seeds and toss until fully coated. Add the bourbon and maple mixture and toss again to coat.
Line a clean baking sheet with foil and spray with nonstick cooking spray. Spread the seeds on the prepared baking sheet and continue to bake until caramelized and dry, an additional 25 to 30 minutes. Cool before serving.
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