1. Heat 1/2 inch vegetable oil in a small skillet over medium heat. Meanwhile, put the flour in a bowl, and season with salt and pepper. Dredge shallot rings in flour all at once. When the oil is hot (a shallot ring will sizzle on contact), fry rings in batches, shaking off excess flour before transferring them to skillet. Fry until golden brown and crisp, 1 to 3 minutes. Transfer shallot rings with tongs or a slotted spoon to paper towels to drain.

2. Heat the extra-virgin olive oil in a Dutch oven or shallow stockpot over medium heat until hot but not smoking. Add spinach (if it doesn't fit all at once, wait to add more until some of it cooks down, or cook in two batches). Season with salt and pepper. Cover; cook, uncovering occasionally to toss, until spinach is wilted, 2 to 3 minutes.

3. Transfer spinach to a serving bowl with tongs or a slotted spoon, leaving any excess liquid in pot. Sprinkle with shallot rings, and serve immediately.