1. Grate peel from lemon and reserve; you should have about 1 tablespoon. Cut lemon in half and squeeze juice into a large bowl, discarding any seeds; fill bowl halfway with water.
2. Break off artichokes' coarse green outer leaves down to tender yellow inner leaves (easily pierced with your fingernail). Cut off thorny tips and pare away fibrous green layers from bottoms. Cut each artichoke into quarters lengthwise; with a spoon, scoop out and discard fuzzy centers. Cut quarters into 1/2-inch wedges (if using baby artichokes, leave quarters whole). As you work, drop pieces into bowl with water and lemon juice.
3. Drain artichokes. In a 10- to 12-inch nonstick frying pan over medium-high heat, stir 2 tablespoons olive oil, garlic, grated lemon and orange peel, and chili flakes until mixture is fragrant, about 2 minutes. Stir in artichokes, 1/2 teaspoon salt, and cracked pepper. Reduce heat to medium and pour in 1/2 cup water; cover and cook until water has been absorbed and artichokes are tender when pierced, about 15 minutes.
4. Remove from heat and stir in vinegar and remaining 2 tablespoons olive oil. Pour into a shallow bowl and let cool to room temperature. Before serving, stir in parsley and add more salt to taste.