Brush a small rimmed baking sheet with olive oil; set aside. In a large pot, bring 6 cups water to a boil over high heat; season with salt. Slowly whisk in polenta, and cook, partially covered, and stirring every 4 to 5 minutes, over medium-low heat until it begins to thicken, 30 to 35 minutes. Remove from heat.
Carefully pour polenta onto prepared baking sheet, spreading it out to an even thickness. Let cool, and tear into 1-inch pieces; lightly dust with flour.
Line a baking sheet with paper towels; set aside. Meanwhile, heat sunflower oil in a large heavy-bottomed pot until it registers 350 degrees on a deep-fry thermometer. Using a slotted spoon, carefully add polenta in batches while maintaining the temperature of the oil. Cook until crispy, about 4 minutes. Transfer to prepared baking sheet to drain. Serve immediately seasoned with sea salt.