Wash the Padron peppers under cold running water, then pat them dry thoroughly with a clean kitchen towel or paper towels to prevent oil splattering.
Heat a large nonstick skillet over medium-high heat. Add the olive oil and swirl to coat the pan; heat until it shimmers but doesn’t smoke.
Arrange the dried peppers in a single layer in the skillet, working in batches if needed so they aren’t crowded.
Cook the peppers for 3 to 5 minutes, turning occasionally with tongs, until their skins blister and char in spots and they soften and wrinkle.
Transfer the hot peppers to a serving plate and immediately sprinkle generously with flaky sea salt.
Serve the peppers immediately while warm as a snack or appetizer, or as part of a tapas-style spread.