2 cups raw nuts (such as almonds, walnuts, pistachios, pecans, and/or blanched hazelnuts)
½ cup raw pumpkin seeds
3 Tbsp. extra-virgin olive oil, plus more for pan
2 cups old-fashioned oats, divided
1¼ cups dried fruit (such as tart cherries, raisins, currants, dates, apricots, and/or blueberries)
¾ cup natural peanut butter (unsalted or low-salt)
½ cup plus 2 Tbsp. honey
2 tsp. kosher salt
2 tsp. vanilla extract
1 large egg white
Preheat oven to 350°. Spread nuts and pumpkin seeds in a 13x9" baking pan and roast until darkened in color and toasty smelling, 10–12 minutes. Transfer nuts and seeds to a food processor and let sit until cool enough to handle.
Reduce oven temperature to 300°. Lightly oil 13x9" pan and line with parchment paper, leaving overhang on both long sides. Lightly oil parchment.
Add 1 cup oats to nut mixture in food processor and pulse until nuts are broken down to a sandy mixture and no whole oats remain. Transfer to a large bowl.
Pulse any dried fruit larger than a raisin in food processor (no need to wipe out) until finely chopped, about the size of chocolate chips. Transfer to bowl with nut mixture. Add remaining 1 cup oats and stir to combine, breaking up any fruit that is stuck together. Add 3 Tbsp. oil and stir to coat. Add peanut butter, but don’t stir it in.
Bring honey, salt, and vanilla to a boil in a medium saucepan (honey will bubble up) over medium heat. Reduce heat to medium-low and simmer, stirring occasionally, until honey is foaming vigorously and smells like caramel, about 3 minutes.
Immediately pour honey syrup over peanut butter in reserved bowl (it will melt the peanut butter). Stir to combine, making sure to aggressively break up any clumps of nut butter.
Stir egg white with a fork or whisk in a small bowl to liquefy. Add to oat mixture and stir until egg white is no longer visible.
Transfer oat mixture to prepared pan and press firmly into an even layer. (Be sure to really compact the mixture into the pan—it helps to use the bottom of a heavy glass or metal measuring cup.)
Bake granola bars until deep golden brown and no longer sticky or wet, 30-35 minutes. Let cool 5 minutes, then lightly score into 16 long rectangles (1 cut lengthwise and 8 cuts crosswise will make bars that are about 6½x1"). Let cool completely in pan, then use parchment to hoist bars out onto a cutting board. Using a sharp chef’s knife, cut along marks to separate bars.
Do Ahead: Bars can be made 1 week ahead. Store airtight at room temperature.