In a medium, heavy-bottomed Dutch oven, add enough oil to come 3 inches up the sides of the pot. Heat until the oil registers 365°F on a deep-fry thermometer. Line a large baking sheet with parchment paper or a nonstick silicone mat and set by the stove.
In a separate medium-sized pot, add the pumpkin seeds, sugar, and ½ cup cold water; bring to a boil over medium-high heat, stirring occasionally to dissolve the sugar. Cook until the liquid reduces to a slightly thick, colorless syrup, 8–10 minutes, then turn off the heat. Using a spider strainer or slotted spoon, remove the seeds from the syrup and carefully transfer them to the pot of oil. Fry until golden, 7–9 minutes, then use the spider strainer to transfer the seeds to the prepared baking sheet in an even layer. Season generously with sea salt, then let cool completely. Break the brittle into bite-size pieces and serve. The brittle can also be stored in an airtight container at room temperature for up to 1 week.